Pith. sign in

REVIEW 4 major objections 3 minor 92 references

On three-dimensional ${\cal N}=4$ supersymmetry: maximally supersymmetric backgrounds and massive deformations

T0 review · 4 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read The paper classifies all maximally supersymmetric 3D N=4 backgrounds into three families, shows the super Cotton scalar X generates massive deformations, and derives topologically massive N=4 gauge theory from one-loop hypermultiplet…

desk verdict Serious superspace paper with a valuable background classification, but Section 7.4's radiative Chern-Simons derivation is algebraically wrong and the new X-only geometry lacks a needed Jacobi check. read the letter →

arxiv 2504.20712 v2 pith:7RCJT6P4 submitted 2025-04-29 hep-th math-phmath.MP

Sergei M. Kuzenko , Emmanouil S. N. Raptakis , Igor B. Samsonov , Gabriele Tartaglino-Mazzucchelli This is my paper · ORCID
classification hep-thmath-phmath.MP
keywords 3DN=4supersymmetryconformalsupergravitysuperCottontensormaximallysupersymmetricbackgroundsdeformedMinkowskisuperspaceprojectiveChern-Simonstheorymassivedeformation
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

Using the SO(N) superspace formulation of three-dimensional N=4 conformal supergravity, the paper sets out to prove that all maximally supersymmetric backgrounds fall into exactly three families, controlled by two superfields: the super Cotton scalar X and the torsion field $S^{{ij i-bar j-bar}}$. It then shows that the same scalar X acts as a universal mass deformation parameter: setting S=0 produces the deformed Minkowski superspace $M^{{3|8}}$_X, and every interacting field theory built there — $\sigma$ models, vector multiplets, and gauge theories — arises as a massive deformation of an N=4 superconformal field theory or of an N=4 gauge theory with SU(2)_L × SU(2)_R R-symmetry, with Chern-Simons terms forced in the gauge sector. The paper also derives topologically massive N=4 gauge theory from one-loop radiative corrections in the hypermultiplet sector, obtaining a Chern-Simons term with a fixed coefficient. If correct, this gives a single object — the vacuum value of the super Cotton tensor — that simultaneously organizes the allowed curved backgrounds and the masses of the matter multiplets on them.

What carries the argument

The load-bearing object is the super Cotton scalar X, defined by $X^{{IJKL}}$=$ε^{{IJKL}}$X for the completely antisymmetric SO(4) tensor that exists for N≥4; it is the superspace extension of the Cotton tensor, and the background is conformally flat if and only if X=0. X enters the N=4 covariant derivative algebra (2.3) as a deformation parameter: it appears in the spinor-derivative anti-commutator and in the R-symmetry curvature, producing the non-centrally extended N=4 Poincaré superalgebra of $M^{{3|8}}$_X. The classification works by imposing the maximal-supersymmetry conditions (3.1) — all Grassmann-odd torsion vanishes and all even torsion is covariantly constant — on the dimension-1 torsion superfields S, X, $S^{{ij i-bar j-bar}}$, $B^{{ij}}$_{$\alpha$ $\beta$} and $C^{{i-bar j-bar}}$_{$\alpha$ $\beta$}, then solving the algebraic constraints (3.5) that follow from integrability. For the field theories, the machinery is projective superspace: left and right projective multiplets on $M^{{3|8}}$_X × $CP^{1}$, defined by analyticity constraints, together with the action principle (6.2) that reduces to the deformed N=2 superspace $M^{{3|4}}$_X.

What would settle it

Compute directly the one-loop parity-odd effective action of the hypermultiplet model (7.25) in the central-charge background (7.1): the paper predicts a Chern-Simons term with coefficient -1/(8π) arising from two spinors whose mass terms have the same sign. A diagrammatic or heat-kernel evaluation that yields a different coefficient, or a cancellation between the Q+ and Q- contributions, would falsify the radiative-generation claim.

Watch

Extended reading notes

Core claim

The central discovery claim is that the super Cotton tensor of N=4 conformal supergravity, which in this case reduces to a single scalar X via $X^{{IJKL}}$=$ε^{{IJKL}}$X, is the organizing object for both geometry and dynamics. The paper shows that every maximally supersymmetric background satisfies one of three sets of conditions: (i) X=0 and $S^{{ij i-bar j-bar}}$=0, which includes the conformally flat (4,0) AdS superspace as well as R×$S^{2}$, AdS_2×R and pp-wave geometries; (ii) X≠0 and $S^{{ij i-bar j-bar}}$=0, giving deformed versions of those spacetimes together with a new geometry, Eq. (3.15), whose Lorentz curvature is proportional to $X^{2}$ and has positive cosmological constant; or (iii) X=0 and $S^{{ij i-bar j-bar}}$≠0, which yields the (2,2) and (3,1) AdS superspaces. On the field-theory side, the paper constructs the most general supersymmetric $\sigma$ models and vector-multiplet/gauge theories on $M^{{3|8}}$_X, the S=0 limit with X≠0, using left and right projective multiplets; these theories are massive deformations of N=4 superconformal field theories and of N=4 gauge theories with SU(2)_L × SU(2)_R R-symmetry, with scalar potential V=($X^{2}$/4)(K_L+K_R) and necessarily present Chern-Simons terms in the gauge sector. Finally, it demonstrates that in the hypermultiplet model the one-loop effective action generates a Chern-Simons term with coefficient -1/(8π), and the full N=4 topologically massive gauge theory emerges radiatively when X=$g^{2}$/(4π).

Load-bearing premise

The classification rests on the assumption, taken from the cited superspace formulation, that the covariant derivative algebra and the maximal-supersymmetry conditions capture every possible background; if that input algebra is incomplete, the three families would not be exhaustive.

Editorial extensions

If this is right

  • If the classification is complete, every rigid N=4 theory on a maximally supersymmetric three-dimensional background sits on one of the three families, so the list of allowed spacetimes for placing such theories — (4,0) AdS, deformed Minkowski, R×S^2, AdS_2×R, pp-wave, and the new X-only geometry — is closed.
  • On M^{3|8}_X every interacting theory is massive: sigma models acquire the scalar potential V=(X^2/4)(K_L+K_R), and gauge theories necessarily develop Chern-Simons terms at the component level, so the deformation parameter X is a universal mass for all multiplets.
  • The one-loop hypermultiplet computation produces a Chern-Simons term with coefficient -1/(8π) regardless of X, and for X=g^2/(4π) the radiative effective action reproduces the classical topologically massive Abelian N=4 gauge theory (7.20).
  • Because X≠0 admits no massless representations, the X→0 limit recovers the standard N=4 superconformal and gauge theories in M^{3|8}, making M^{3|8}_X a one-parameter family of massive deformations that connects to the undeformed theory.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The mirror map (2.4) flips the sign of X and swaps the left and right sectors, so the classification should be symmetric under it; in particular, the novel X-only geometry (3.15) presumably has a mirror counterpart built from C^{i-bar j-bar} with the same positive-curvature property, a consequence the paper does not spell out.
  • Whether the radiative Chern-Simons term appears depends on the realization of the central charge: in the paper's background (7.1) the two hypermultiplet spinors get same-sign masses, whereas in earlier models where the central charge is a physical vector-multiplet vev their contributions cancel; a natural testable extension is to map out exactly which realizations give add-up versus cancellation.
  • If an explicit metric can be extracted from (3.15), the new positive-curvature background could serve as a rigid spacetime for localization; extending the S^3 partition-function calculations to this X-only geometry would give exact results that interpolate between massive deformed theories and the standard ones as X→0.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 3 minor

Summary. This paper develops a superspace description of three-dimensional N=4 conformal supergravity and uses it to classify maximally supersymmetric backgrounds. The classification is organized by the super Cotton scalar X and the tensor S^{ij i-bar j-bar}: (i) X=0 and S^{ij i-bar j-bar}=0; (ii) X≠0 and S^{ij i-bar j-bar}=0; (iii) X=0 and S^{ij i-bar j-bar}≠0. Within case (ii) the paper describes deformed R×S^2, AdS_2×R, and pp-wave geometries, as well as a new X-only background with positive Lorentz curvature, Eq. (3.15). The paper then constructs field theories on the deformed Minkowski superspace M^{3|8}_X using projective superspace techniques: hyperkähler-cone sigma models with an X^2 scalar potential, vector multiplet models with Chern–Simons terms, and N=4 super Yang–Mills Chern–Simons theory in N=2 superfield form. Finally, the paper claims that a topologically massive N=4 gauge theory is generated from one-loop hypermultiplet radiative corrections.

Significance. If the classification and the radiative-generation result are correct, the paper provides the first complete list of maximally supersymmetric N=4 backgrounds and demonstrates a robust framework for massive deformations with non-central supersymmetry. The projective-superspace constructions, the explicit N=2 reductions, the component action in Appendix C, and the separation of the three classification branches are valuable and largely explicit. The paper also gives a concrete mechanism connecting the super Cotton expectation value X to massive deformations, which is a substantive extension of earlier work. However, the two most striking claims—the new X-only background and the one-loop derivation of topologically massive N=4 gauge theory—rest on points that are currently either asserted without proof or algebraically incorrect as written. These points need to be repaired before the central claims can be accepted.

major comments (4)
  1. [Section 3.2, Eqs. (3.15)–(3.16)] The existence of the X-only background (3.15) is the principal new classification result, but its consistency is dismissed with the statement that the covariant derivatives satisfy the Jacobi identities (3.16), without a calculation. The nontrivial part is not the bosonic commutator [D_a, D_b]; it is the mixed Jacobi identities involving D^{i i-bar}_α together with D_{βγ}, and the compatibility of the R-symmetry curvature term -X ε_{abc} B^{c}_{ij} L^{ij} with the Lorentz curvature term X^2 M_{ab}. Please provide the full Jacobi verification, including an explicit check that no extra conditions on X or B beyond (3.11) are forced. Without this, the claim that this is a maximally supersymmetric background is not established.
  2. [Section 3.1, Eq. (3.6)] The inference that B^{ij}_{αβ} C^{i-bar j-bar}_{αβ}=0 implies that at least one of B^{ij}_{αβ} or C^{i-bar j-bar}_{αβ} must vanish is not justified as written. The contraction is over spinor indices only, since the L and R isospin indices are independent, so two non-zero rank-2 symmetric spinors can be orthogonal. The other equations in (3.6) do not visibly exclude this possibility. Please supply the missing argument, or explicitly list the additional branches if they exist. This step is load-bearing for the claimed three-family classification.
  3. [Section 7.4, Eqs. (7.35)–(7.36)] The step from the coincident-point propagator (7.35) to the parity-odd current (7.36) is algebraically incorrect. Substituting (7.35) into (7.31) gives ⟨J⟩_odd = -(1/8π)(1/|X+G| - 1/|X-G|), which is not equal to -(1/8π)((X+G)-(X-G)). Even if the absolute values are dropped, the sum is -(1/8π)(1/(X+G) - 1/(X-G)) = G/[4π(X^2-G^2)], not -G/(4π). Thus Eq. (7.36) does not follow from Eq. (7.35), and the subsequent derivation of the Chern–Simons action (7.37) and its N=4 completion (7.38) is not valid as presented. A corrected one-loop computation, with all approximations clearly stated, is required before the radiative-generation claim can be accepted.
  4. [Section 2, Eq. (2.3)] The completeness of the background classification is conditional on the assumption that the algebra (2.3), taken from Ref. [15], contains all relevant dimension-1 torsion superfields and that the conditions (3.1) fully characterize maximal supersymmetry. The paper explicitly says that the Bianchi identities are not used. This is acceptable only if the completeness of (2.3) has been established in the cited work; the revised manuscript should state this clearly, and ideally check that no dimension-1 torsion superfield relevant to maximally supersymmetric backgrounds has been omitted.
minor comments (3)
  1. [Section 5.4.1] The sentence describing the right polar multiplet transformation contains a duplicated article: 'the the left transformation laws (5.28)' should read 'the left transformation laws (5.28)'.
  2. [Footnote 3] The word 'maxiamlly' in the phrase 'maxiamlly supersymmetric solutions' is a typo for 'maximally supersymmetric solutions'.
  3. [Section 7.3, Eq. (7.28)] The equal sign of the mass terms for χ_+ and χ_- is crucial for the later cancellation argument; a one-line derivation or comment explaining why the central charge realization produces the same sign would help the reader verify this point.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: background classification and massive deformations are derived from the stated superspace algebra and explicit one-loop calculations, not from their conclusions.

full rationale

The paper's central claims are conditional on the 3D N=4 conformal-supergravity covariant-derivative algebra (2.3), quoted from Ref. [15], and on the standard characterization of maximally supersymmetric backgrounds (3.1) from Refs. [43,44]. These are stated inputs, not outputs. Section 3 solves the algebraic conditions (3.5) that follow from (3.1), producing three branches (X=S^{ij i-bar j-bar}=0; X nonzero with S^{ij i-bar j-bar}=0; X=0 with S^{ij i-bar j-bar} nonzero) and, within case (ii), the X-only commutator (3.15). Nothing in that derivation adjusts X or the torsion superfields to match a pre-selected background; X is a background value of the super-Cotton scalar. The massive-deformation sections likewise take the deformed algebra (1.1) as the starting point and construct projective-multiplet actions and component Lagrangians (e.g., V = (1/4)X^2(K_L+K_R) in Eq. (6.34)) directly from the algebra. The one-loop generation of topologically massive N=4 gauge theory is a concrete calculation: Eq. (7.35) computes the hypermultiplet current and Eq. (7.37) fixes the Chern-Simons coefficient -1/(8*pi); the N=4 completion (7.38) is then fixed by the independently defined SUSY transformations (7.16), not by fitting. The paper relies heavily on the authors' prior framework, but the cited results are published, parameter-free results whose assumptions do not include the new classification or the one-loop coefficients. The asserted Jacobi-identity check for Eq. (3.15) (Sec. 3.2) is unshown, but a missing verification is a rigor or correctness issue, not circularity, because no equation is being reused as its own output. Accordingly no circular step can be exhibited.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central results rest on the superspace framework of [15] and projective superspace techniques of [15,18,23]. The only external parameters are the background constants S and X; no data fitting is used. No new particles, forces, or dimensions are postulated.

free parameters (2)
  • X
    Constant value of the super Cotton scalar, the deformation parameter of M^{3|8}_X. A background input, not fitted to data, but central to the classification and massive deformations.
  • S
    Constant determining the AdS curvature in the (4,0) AdS superspace. A background input used throughout the classification.
assumptions (4)
  • domain assumption The N=4 conformal supergravity covariant derivative algebra (2.3) is complete, containing torsion superfields S, X, S^{ij i-bar j-bar}, B^{ij}_{alpha beta}, C^{i-bar j-bar}_{alpha beta}.
    The paper takes this algebra from [15] and uses it for the classification (Section 2), explicitly not deriving the full Bianchi identities. If a torsion superfield is missing, the classification could be incomplete.
  • domain assumption Maximally supersymmetric backgrounds are characterized by (3.1): all Grassmann-odd torsion components vanish and Grassmann-even torsion components are annihilated by spinor covariant derivatives.
    Criterion from [43,44] used in Section 3 to derive the integrability conditions (3.5).
  • domain assumption The projective superspace action principle (6.2) is a valid off-shell N=4 action on M^{3|8}_X.
    All model constructions in Sections 6 and 7 rely on this action principle, taken from [15,18].
  • domain assumption N=4 sigma model target spaces are hyperkahler cones with homothetic conformal Killing vectors.
    Used in Section 6.1 for the potential V = X^2(K_L+K_R)/4, following [18].

how reviews work

0 comments
Cite this review

Pith. "Pith review of On three-dimensional ${\cal N}=4$ supersymmetry: maximally supersymmetric backgrounds and massive deformations." pith.science (2026). https://pith.science/paper/7RCJT6P4

@misc{pith2026250420712,
  author       = {Pith},
  title        = {Pith review of: On three-dimensional $\cal N=4$ supersymmetry: maximally supersymmetric backgrounds and massive deformations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7RCJT6P4}},
  note         = {Machine review of arXiv:2504.20712}
}
abstract

Using the $SO ({\cal N})$ superspace formulation for $\cal N$-extended conformal supergravity in three dimensions, we derive all maximally supersymmetric backgrounds in the ${\cal N} =4$ case. The specific feature of this choice is that the so-called super Cotton tensor $X^{IJKL} = X^{[IJKL]}$, which exists for ${\cal N} \geq 4$, is equivalent to the scalar $X$ defined by $X^{IJKL} = \varepsilon^{IJKL} X$. This scalar may be used as a deformation parameter. In the family of $(p,q)$ anti-de Sitter (AdS) superspaces with $p+q=4$, it is known that $X\neq 0$ exists only if $p=4$ and $q=0$. In general, the $(4,0)$ AdS superspaces are characterised by the structure group $SL(2,{\mathbb R}) \times SO (4)$ and their geometry is determined by two constant parameters, $S$ and $X$, of which the former determines the AdS curvature, while the $R$-symmetry curvature is determined by the parameters $(X+2S)$ and $(X-2S)$ in the left and right sectors of $SU(2)_{\rm L} \times SU(2)_{\rm R}$, respectively. Setting $S=0$ leads to the so-called deformed ${\cal N}=4$ Minkowski superspace ${\mathbb M}^{3|8}_X$ introduced thirteen years ago. We construct general interacting supersymmetric field theories in ${\mathbb M}^{3|8}_X$ and demonstrate that they originate as massive deformations of the following two families of ${\cal N} =4$ theories in standard Minkowski superspace ${\mathbb M}^{3|8}$: (i) ${\cal N}=4$ superconformal field theories; and (ii) ${\cal N}=4$ supersymmetric gauge theories in ${\mathbb M}^{3|8}$ which are not superconformal but possess the $R$-symmetry group $SU(2)_{\rm L} \times SU(2)_{\rm R}$. Extensions of the theories in (ii) to ${\mathbb M}^{3|8}_X$ necessarily contain Chern-Simons terms at the component level. We also demonstrate the generation of topologically massive ${\cal N}=4$ supersymmetric gauge theories from radiative corrections in the hypermultiplet sector.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

92 extracted references · 36 canonical work pages

  1. [15]

    Off-shell supergravity-matter couplings in three dimensions,

    S. M. Kuzenko, U. Lindstr¨ om and G. Tartaglino-Mazzucchelli, “Off-shell supergravity-matter couplings in three dimensions,” JHEP 1103, 120 (2011)] [arXiv:1101.4013 [hep-th]]

    arXiv 2011

  2. [1]

    Gauge dynamics and compactification to three dimensions,

    N. Seiberg and E. Witten, “Gauge dynamics and compactification to three dimensions,” [arXiv:hep- th/9607163]. 48

    work page arXiv

  3. [2]

    On mirror symmetry in three-dimensional Abelian gauge theories,

    A. Kapustin and M. J. Strassler, “On mirror symmetry in three-dimensional Abelian gauge theories,” JHEP 04, 021 (1999) [arXiv:hep-th/9902033]]

    arXiv 1999

  4. [3]

    Mirror symmetry in three-dimensional gauge theories,

    K. A. Intriligator and N. Seiberg, “Mirror symmetry in three-dimensional gauge theories,” Phys. Lett. B 387, 513 (1996) [arXiv:hep-th/9607207]

    arXiv 1996

  5. [4]

    Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynam- ics,

    A. Hanany and E. Witten, “Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynam- ics,” Nucl. Phys. B 492, 152 (1997) [arXiv:hep-th/9611230]

    arXiv 1997

  6. [5]

    The Coulomb branch of 3d N = 4 theories,

    M. Bullimore, T. Dimofte, and D. Gaiotto, “The Coulomb branch of 3d N = 4 theories,” Commun. Math. Phys. 354, 671 (2017) [arXiv:1503.04817 [hep-th]]

    arXiv 2017

  7. [6]

    Three-dimensional massive gauge theories,

    S. Deser, R. Jackiw and S. Templeton, “Three-dimensional massive gauge theories,” Phys. Rev. Lett. 48, 975 (1982)

    1982

  8. [7]

    Gauge noninvariance and parity nonconservation of three-dimensional fermions,

    A. N. Redlich, “Gauge noninvariance and parity nonconservation of three-dimensional fermions,” Phys. Rev. Lett. 52, 18 (1984)

    1984

Show all 92 references
  1. [8]

    Axial-anomaly-induced fermion fractionization and effective gauge theory actions in odd-dimensional space-times,

    A. J. Niemi and G. W. Semenoff, “Axial-anomaly-induced fermion fractionization and effective gauge theory actions in odd-dimensional space-times,” Phys. Rev. Lett. 51, 2077 (1983)

    1983

  2. [9]

    Parity violation and gauge noninvariance of the effective gauge field action in three dimensions,

    A. N. Redlich, “Parity violation and gauge noninvariance of the effective gauge field action in three dimensions,” Phys. Rev. D 29, 2366 (1984)

    1984

  3. [10]

    Chern-Simons theories with supersymmetries in three-dimensions,

    H. Nishino and S. J. Gates, Jr., “Chern-Simons theories with supersymmetries in three-dimensions,” Int. J. Mod. Phys. A 8, 3371 (1993)

    1993

  4. [11]

    Chern-Simons matter systems with manifest N=2 supersymmetry,

    E. A. Ivanov, “Chern-Simons matter systems with manifest N=2 supersymmetry,” Phys. Lett. B 268, 203 (1991)

    1991

  5. [12]

    Notes on superconformal Chern-Simons-matter theories,

    D. Gaiotto and X. Yin, “Notes on superconformal Chern-Simons-matter theories,” JHEP 08, 056 (2007) [arXiv:0704.3740 [hep-th]]

    2007 arXiv

  6. [13]

    N=4 Superconformal Chern-Simons theories with hyper and twisted hyper multiplets,

    K. Hosomichi, K. M. Lee, S. Lee, S. Lee and J. Park, “N=4 Superconformal Chern-Simons theories with hyper and twisted hyper multiplets,” JHEP 07, 091 (2008) [arXiv:0805.3662 [hep-th]]

    2008 arXiv

  7. [14]

    N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,

    O. Aharony, O. Bergman, D. L. Jafferis and J. Maldacena, “N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals,” JHEP 10, 091 (2008) [arXiv:0806.1218 [hep-th]]

    2008 arXiv

  8. [16]

    Superfield theories on S3 and their localization,

    I. B. Samsonov and D. Sorokin, “Superfield theories on S3 and their localization,” JHEP 04, 102 (2014) [arXiv:1401.7952 [hep-th]]

    2014 arXiv

  9. [17]

    N=4 supersymmetric Yang-Mills theories in AdS3,

    S. M. Kuzenko and G. Tartaglino-Mazzucchelli, “N=4 supersymmetric Yang-Mills theories in AdS3,” JHEP 05, 018 (2014) [arXiv:1402.3961 [hep-th]]

    2014 arXiv

  10. [18]

    Nonlinear sigma models with AdS supersym- metry in three dimensions,

    D. Butter, S. M. Kuzenko and G. Tartaglino-Mazzucchelli, “Nonlinear sigma models with AdS supersym- metry in three dimensions,” JHEP 02, 121 (2013) [arXiv:1210.5906 [hep-th]]

    2013 arXiv

  11. [19]

    Conformal supergravity in three dimensions: New off-shell formulation,

    D. Butter, S. M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, “Conformal supergravity in three dimensions: New off-shell formulation,” JHEP 09, 072 (2013) [arXiv:1305.3132 [hep-th]]. 49

    2013 arXiv

  12. [20]

    Conformal supergravity in three dimensions: Off-shell actions,

    D. Butter, S. M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, “Conformal supergravity in three dimensions: Off-shell actions,” JHEP 10, 073 (2013) [arXiv:1306.1205 [hep-th]]

    2013 arXiv

  13. [21]

    N=6 superconformal gravity in three dimen- sions from superspace,

    S. M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, “N=6 superconformal gravity in three dimen- sions from superspace,” JHEP 01, 121 (2014) [arXiv:1308.5552 [hep-th]]

    2014 arXiv

  14. [22]

    Three-dimensional N = 2 supergravity theories: From superspace to components,

    S. M. Kuzenko, U. Lindstr¨ om, M. Rocek, I. Sachs and G. Tartaglino-Mazzucchelli, “Three-dimensional N = 2 supergravity theories: From superspace to components,” Phys. Rev. D 89, 085028 (2014) [arXiv:1312.4267 [hep-th]]

    2014 arXiv

  15. [23]

    Three-dimensional (p,q) AdS superspaces and matter couplings,

    S. M. Kuzenko, U. Lindstr¨ om and G. Tartaglino-Mazzucchelli, “Three-dimensional (p,q) AdS superspaces and matter couplings,” JHEP 1208, 024 (2012) [arXiv:1205.4622 [hep-th]]

    2012 arXiv

  16. [24]

    Three-dimensional N=2 (AdS) supergravity and associ- ated supercurrents,

    S. M. Kuzenko and G. Tartaglino-Mazzucchelli, “Three-dimensional N=2 (AdS) supergravity and associ- ated supercurrents,” JHEP 1112, 052 (2011) [arXiv:1109.0496 [hep-th]]

    2011 arXiv

  17. [25]

    D=3, N=8 conformal supergravity and the Dragon window,

    M. Cederwall, U. Gran and B. E. W. Nilsson, “D=3, N=8 conformal supergravity and the Dragon window,” JHEP 09, 101 (2011) [arXiv:1103.4530 [hep-th]]

    2011 arXiv

  18. [26]

    Maximal supergravity in three dimensions: supergeometry and differential forms,

    J. Greitz and P. S. Howe, “Maximal supergravity in three dimensions: supergeometry and differential forms,” JHEP 07, 071 (2011) [arXiv:1103.2730 [hep-th]]

    2011 arXiv

  19. [27]

    Notes on SUSY gauge theories on three-sphere,

    N. Hama, K. Hosomichi and S. Lee, “Notes on SUSY gauge theories on three-sphere,” JHEP 1103, 127 (2011) [arXiv:1012.3512 [hep-th]]

    2011 arXiv

  20. [28]

    Gauge and matter superfield theories on S2,

    I. B. Samsonov and D. Sorokin, “Gauge and matter superfield theories on S2,” JHEP 09, 097 (2014) [arXiv:1407.6270 [hep-th]]

    2014 arXiv

  21. [29]

    A Chern-Simons action for three-dimensional anti-de Sitter super- gravity theories,

    A. Ach´ ucarro and P. K. Townsend, “A Chern-Simons action for three-dimensional anti-de Sitter super- gravity theories,” Phys. Lett. B 180, 89 (1986)

    1986

  22. [30]

    New supergravities with central charges and Killing spinors in 2+1 dimensions,

    P. S. Howe, J. M. Izquierdo, G. Papadopoulos and P. K. Townsend, “New supergravities with central charges and Killing spinors in 2+1 dimensions,” Nucl. Phys. B 467, 183 (1996) [arXiv:hep-th/9505032]

    1996 arXiv

  23. [31]

    On the superconformal flatness of AdS superspaces,

    I. A. Bandos, E. Ivanov, J. Lukierski and D. Sorokin, “On the superconformal flatness of AdS superspaces,” JHEP 06, 040 (2002) [arXiv:hep-th/0205104 [hep-th]]

    2002 arXiv

  24. [32]

    Minimal N = 4 topologically massive supergravity,

    S. M. Kuzenko, J. Novak and I. Sachs, “Minimal N = 4 topologically massive supergravity,” JHEP 03, 109 (2017) [arXiv:1610.09895 [hep-th]]

    2017 arXiv

  25. [33]

    Supersymmetries and their representations,

    W. Nahm, “Supersymmetries and their representations,” Nucl. Phys. B 135, 149 (1978)

    1978

  26. [34]

    A new maximally supersymmetric background of IIB superstring theory,

    M. Blau, J. M. Figueroa-O’Farrill, C. Hull and G. Papadopoulos, “A new maximally supersymmetric background of IIB superstring theory,” JHEP 0201, 047 (2002) [arXiv:hep-th/0110242]

    2002 arXiv

  27. [35]

    I-brane dynamics,

    N. Itzhaki, D. Kutasov and N. Seiberg, “I-brane dynamics,” JHEP 0601, 119 (2006) [hep-th/0508025]

    2006 arXiv

  28. [36]

    Fivebranes from gauge theory,

    H. Lin and J. M. Maldacena, “Fivebranes from gauge theory,” Phys. Rev. D 74, 084014 (2006) [arXiv:hep- th/0509235]

    2006

  29. [37]

    Matrix theory of type IIB plane wave from membranes,

    J. Gomis, A. J. Salim and F. Passerini, “Matrix theory of type IIB plane wave from membranes,” JHEP 0808, 002 (2008) [arXiv:0804.2186 [hep-th]]. 50

    2008 arXiv

  30. [38]

    Mass-deformed Bagger-Lambert theory and its BPS objects,

    K. Hosomichi, K. -M. Lee and S. Lee, “Mass-deformed Bagger-Lambert theory and its BPS objects,” Phys. Rev. D 78, 066015 (2008) [arXiv:0804.2519 [hep-th]]

    2008 arXiv

  31. [39]

    A topologically massive gauge theory with 32 supercharges,

    E. A. Bergshoeff and O. Hohm, “A topologically massive gauge theory with 32 supercharges,” Phys. Rev. D 78, 125017 (2008) [arXiv:0810.0377 [hep-th]]

    2008 arXiv

  32. [40]

    3d N = 4 mirror symmetry, TQFTs, and ’t Hooft anomaly matching,

    M. K.N. Balasubramanian, A. Banerjee, M. Buican, Z. Duan, A. E. V. Ferrari and H. Jiang, “3d N = 4 mirror symmetry, TQFTs, and ’t Hooft anomaly matching,” [arXiv:2412.21066 [hep-th]]

    arXiv

  33. [41]

    Time-reversal invariant TQFTs from self-mirror symmetric SCFTs,

    H. Jiang, “Time-reversal invariant TQFTs from self-mirror symmetric SCFTs,” [arXiv:2501.00460 [hep- th]]

    arXiv

  34. [42]

    Deformations of superconformal theories,

    C. Cordova, T. T. Dumitrescu and K. Intriligator, “Deformations of superconformal theories,” JHEP 11, 135 (2016) [arXiv:1602.01217 [hep-th]]

    2016 arXiv

  35. [43]

    Symmetries of curved superspace in five dimensions,

    S. M. Kuzenko, J. Novak and G. Tartaglino-Mazzucchelli, “Symmetries of curved superspace in five dimensions,” JHEP 10, 175 (2014) [arXiv:1406.0727 [hep-th]]

    2014 arXiv

  36. [44]

    Supersymmetric spacetimes from curved superspace,

    S. M. Kuzenko, “Supersymmetric spacetimes from curved superspace,” PoS CORFU2014, 140 (2015) [arXiv:1504.08114 [hep-th]]

    2015 arXiv

  37. [45]

    I. L. Buchbinder and S. M. Kuzenko, Ideas and Methods of Supersymmetry and Supergravity, Or a Walk Through Superspace, IOP, Bristol, 1998

    1998

  38. [46]

    Symmetries of N = (1, 0) supergravity backgrounds in six dimensions,

    S. M. Kuzenko, U. Lindstr¨ om, E. S. N. Raptakis and G. Tartaglino-Mazzucchelli, “Symmetries of N = (1, 0) supergravity backgrounds in six dimensions,” JHEP 03, 157 (2021) [arXiv:2012.08159 [hep-th]]

    2021 arXiv

  39. [47]

    Rigid supersymmetric theories in curved superspace,

    G. Festuccia and N. Seiberg, “Rigid supersymmetric theories in curved superspace,” JHEP 06, 114 (2011) [arXiv:1105.0689 [hep-th]]

    2011 arXiv

  40. [48]

    Rigid 4D N = 2 supersymmetric backgrounds and actions,

    D. Butter, G. Inverso and I. Lodato, “Rigid 4D N = 2 supersymmetric backgrounds and actions,” JHEP 09, 088 (2015) [arXiv:1505.03500 [hep-th]]

    2015 arXiv

  41. [49]

    Supersymmetric field theories on three- manifolds,

    C. Closset, T. T. Dumitrescu, G. Festuccia and Z. Komargodski, “Supersymmetric field theories on three- manifolds,” JHEP 05, 017 (2013) [arXiv:1212.3388 [hep-th]]

    2013 arXiv

  42. [50]

    An introduction to supersymmetric field theories in curved space,

    T. T. Dumitrescu, “An introduction to supersymmetric field theories in curved space,” J. Phys. A 50, no.44, 443005 (2017) [arXiv:1608.02957 [hep-th]]

    2017 arXiv

  43. [51]

    Supergravity-matter actions in three dimensions and Chern-Simons terms,

    S. M. Kuzenko and J. Novak, “Supergravity-matter actions in three dimensions and Chern-Simons terms,” JHEP 05, 093 (2014) [arXiv:1401.2307 [hep-th]]

    2014 arXiv

  44. [52]

    Off-shell superconformal nonlinear sigma-models in three dimensions,

    S. M. Kuzenko, J. H. Park, G. Tartaglino-Mazzucchelli and R. Unge, “Off-shell superconformal nonlinear sigma-models in three dimensions,” JHEP 01, 146 (2011) [arXiv:1011.5727 [hep-th]]

    2011 arXiv

  45. [53]

    Harmonic superpotentials and symmetries in gauge theories with eight supercharges,

    B. Zupnik, “Harmonic superpotentials and symmetries in gauge theories with eight supercharges,” Nucl. Phys. B 554, 365 (1999) [Erratum-ibid. B 644, 405 (2002)] [arXiv:hep-th/9902038]

    1999 arXiv

  46. [54]

    Three-dimensional N=4 superconformal superfield theories,

    B. M. Zupnik, “Three-dimensional N=4 superconformal superfield theories,” Theor. Math. Phys. 162, 74 (2010) [arXiv:0905.1179 [hep-th]]

    2010 arXiv

  47. [55]

    Harmonic superspaces for three-dimensional theories,

    B. M. Zupnik, “Harmonic superspaces for three-dimensional theories,” in: Supersymmetries and Quantum Symmetries, J. Wess and E. Ivanov (Eds.), Springer, Berlin, 1999, pp. 116–123, [arXiv:hep-th/9804167 [hep-th]]. 51

    1999 arXiv

  48. [56]

    Killing superalgebras for Lorentzian four-manifolds,

    P. de Medeiros, J. Figueroa-O’Farrill and A. Santi, “Killing superalgebras for Lorentzian four-manifolds,” JHEP 06, 106 (2016) [arXiv:1605.00881 [hep-th]]

    2016 arXiv

  49. [57]

    Self-interacting tensor multiplets in N=2 superspace,

    A. Karlhede, U. Lindstr¨ om and M. Roˇ cek, “Self-interacting tensor multiplets in N=2 superspace,” Phys. Lett. B 147, 297 (1984)

    1984

  50. [58]

    New hyperk¨ ahler metrics and new supermultiplets,

    U. Lindstr¨ om and M. Roˇ cek, “New hyperk¨ ahler metrics and new supermultiplets,” Commun. Math. Phys. 115, 21 (1988)

    1988

  51. [59]

    N=2 super Yang-Mills theory in projective superspace,

    U. Lindstr¨ om and M. Roˇ cek, “N=2 super Yang-Mills theory in projective superspace,” Commun. Math. Phys. 128, 191 (1990)

    1990

  52. [60]

    Feynman rules in N = 2 projective superspace. I: Massless hypermultiplets,

    F. Gonzalez-Rey, M. Roˇ cek, S. Wiles, U. Lindstr¨ om and R. von Unge, “Feynman rules in N = 2 projective superspace. I: Massless hypermultiplets,” Nucl. Phys. B 516, 426 (1998) [arXiv:hep-th/9710250]

    1998 arXiv

  53. [61]

    Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace,

    A. S. Galperin, E. A. Ivanov, S. N. Kalitzin, V. Ogievetsky, E. Sokatchev, “Unconstrained N=2 matter, Yang-Mills and supergravity theories in harmonic superspace,” Class. Quant. Grav. 1, 469 (1984)

    1984

  54. [62]

    A. S. Galperin, E. A. Ivanov, V. I. Ogievetsky and E. S. Sokatchev, Harmonic Superspace, Cambridge University Press, Cambridge, 2001

    2001

  55. [63]

    Projective superspace as a double-punctured harmonic superspace,

    S. M. Kuzenko, “Projective superspace as a double-punctured harmonic superspace,” Int. J. Mod. Phys. A 14, 1737 (1999) [arXiv:hep-th/9806147]

    1999 arXiv

  56. [64]

    Deriving projective hyperspace from harmonic,

    D. Jain and W. Siegel, “Deriving projective hyperspace from harmonic,” Phys. Rev. D 80 (2009), 045024 [arXiv:0903.3588 [hep-th]]

    2009 arXiv

  57. [65]

    Lectures on nonlinear sigma-models in projective superspace,

    S. M. Kuzenko, “Lectures on nonlinear sigma-models in projective superspace,” J. Phys. A 43, 443001 (2010) [arXiv:1004.0880 [hep-th]]

    2010 arXiv

  58. [66]

    Relating harmonic and projective descriptions of N=2 nonlinear sigma models,

    D. Butter, “Relating harmonic and projective descriptions of N=2 nonlinear sigma models,” JHEP 11 (2012), 120 [arXiv:1206.3939 [hep-th]]

    2012 arXiv

  59. [67]

    N=2 supersymmetric sigma models and duality,

    S. M. Kuzenko, “N=2 supersymmetric sigma models and duality,” JHEP 1001, 115 (2010) [arXiv:0910.5771 [hep-th]]

    2010 arXiv

  60. [68]

    The CNM-hypermultiplet nexus,

    S. J. Gates Jr. and S. M. Kuzenko, “The CNM-hypermultiplet nexus,” Nucl. Phys. B 543, 122 (1999) [arXiv:hep-th/9810137]

    1999 arXiv

  61. [69]

    4D N = 2 supersymmetric off-shell sigma models on the cotangent bundles of K¨ ahler manifolds,

    S. J. Gates Jr. and S. M. Kuzenko, “4D N = 2 supersymmetric off-shell sigma models on the cotangent bundles of K¨ ahler manifolds,” Fortsch. Phys.48, 115 (2000) [arXiv:hep-th/9903013]

    2000 arXiv

  62. [70]

    Hyper-K¨ ahler sigma models on (co)tangent bundles with SO(n) isometry,

    M. Arai and M. Nitta, “Hyper-K¨ ahler sigma models on (co)tangent bundles with SO(n) isometry,” Nucl. Phys. B 745, 208 (2006) [arXiv:hep-th/0602277]

    2006 arXiv

  63. [71]

    Hyperk¨ ahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace,

    M. Arai, S. M. Kuzenko and U. Lindstr¨ om, “Hyperk¨ ahler sigma models on cotangent bundles of Hermitian symmetric spaces using projective superspace,” JHEP 0702, 100 (2007) [arXiv:hep-th/0612174]

    2007 arXiv

  64. [72]

    Polar supermultiplets, Hermitian symmetric spaces and hyperk¨ ahler metrics,

    M. Arai, S. M. Kuzenko and U. Lindstr¨ om, “Polar supermultiplets, Hermitian symmetric spaces and hyperk¨ ahler metrics,” JHEP0712, 008 (2007) [arXiv:0709.2633 [hep-th]]

    2007 arXiv

  65. [73]

    Chiral formulation for hyperk¨ ahler sigma-models on cotangent bundles of symmetric spaces,

    S. M. Kuzenko and J. Novak, “Chiral formulation for hyperk¨ ahler sigma-models on cotangent bundles of symmetric spaces,” JHEP 0812, 072 (2008) [arXiv:0811.0218 [hep-th]]. 52

    2008 arXiv

  66. [74]

    On N=2 supergravity and projective superspace: Dual formulations,

    S. M. Kuzenko, “On N=2 supergravity and projective superspace: Dual formulations,” Nucl. Phys. B 810, 135 (2009) [arXiv:0807.3381 [hep-th]]

    2009 arXiv

  67. [75]

    The improved tensor multiplet in N = 2 supergravity,

    B. de Wit, R. Philippe and A. Van Proeyen, “The improved tensor multiplet in N = 2 supergravity,” Nucl. Phys. B 219, 143 (1983)

    1983

  68. [76]

    Scalar tensor duality and N =1,2 non-linearσ-models,

    U. Lindstr¨ om and M. Roˇ cek, “Scalar tensor duality and N =1,2 non-linearσ-models,” Nucl. Phys. B 222, 285 (1983)

    1983

  69. [77]

    Hyperk¨ ahler metrics and supersymmetry,

    N. J. Hitchin, A. Karlhede, U. Lindstr¨ om and M. Roˇ cek, “Hyperk¨ ahler metrics and supersymmetry,” Commun. Math. Phys. 108, 535 (1987)

    1987

  70. [78]

    Hypermultiplets, hyperk¨ ahler cones and quaternion-K¨ ahler geometry,

    B. de Wit, M. Roˇ cek and S. Vandoren, “Hypermultiplets, hyperk¨ ahler cones and quaternion-K¨ ahler geometry,” JHEP 0102, 039 (2001) [arXiv:hep-th/0101161]

    2001 arXiv

  71. [79]

    The structure of N=2 supersymmetric nonlinear sigma models in AdS 4,

    D. Butter and S. M. Kuzenko, “The structure of N=2 supersymmetric nonlinear sigma models in AdS 4,” JHEP 11, 080 (2011) [arXiv:1108.5290 [hep-th]]

    2011 arXiv

  72. [80]

    Low-energy effective actions in three-dimensional extended SYM theories,

    I. L. Buchbinder, N. G. Pletnev and I. B. Samsonov, “Low-energy effective actions in three-dimensional extended SYM theories,” JHEP 01, 121 (2011) [[arXiv:1010.4967 [hep-th]]

    2011 arXiv

  73. [81]

    Extended supersymmetry and super-BF gauge theories,

    R. Brooks and S. J. Gates Jr., “Extended supersymmetry and super-BF gauge theories,” Nucl. Phys. B 432, 205 (1994) [arXiv:hep-th/9407147]

    1994 arXiv

  74. [82]

    New higher-derivative couplings in 4D N = 2 supergravity,

    D. Butter and S. M. Kuzenko, “New higher-derivative couplings in 4D N = 2 supergravity,” JHEP 03, 047 (2011) [arXiv:1012.5153 [hep-th]]

    2011 arXiv

  75. [83]

    S. J. Gates, Jr., M. T. Grisaru, M. Roˇ cek and W. Siegel, Superspace, or One Thousand and One Lessons in Supersymmetry, Front. Phys. 58, 1 (1983) [arXiv:hep-th/0108200]

    1983 arXiv

  76. [84]

    Effective action of three-dimensional extended supersymmetric matter on gauge superfield background,

    I. L. Buchbinder, N. G. Pletnev and I. B. Samsonov, “Effective action of three-dimensional extended supersymmetric matter on gauge superfield background,” JHEP 04, 124 (2010) [arXiv:1003.4806 [hep- th]]

    2010 arXiv

  77. [85]

    Two-loop low-energy effective actions in N=2 and N=4 three-dimensional SQED,

    I. L. Buchbinder, B. S. Merzlikin and I. B. Samsonov, “Two-loop low-energy effective actions in N=2 and N=4 three-dimensional SQED,” JHEP 07, 012 (2013) [arXiv:1305.4815 [hep-th]]

    2013 arXiv

  78. [86]

    Two-loop low-energy effective action in Abelian supersymmetric Chern-Simons matter models,

    I. L. Buchbinder, B. S. Merzlikin and I. B. Samsonov, “Two-loop low-energy effective action in Abelian supersymmetric Chern-Simons matter models,” Nucl. Phys. B 881, 42 (2014) [arXiv:1311.5001 [hep-th]]

    2014 arXiv

  79. [87]

    On the background field method beyond one loop: A manifestly covariant derivative expansion in super Yang-Mills theories,

    S. M. Kuzenko and I. N. McArthur, “On the background field method beyond one loop: A manifestly covariant derivative expansion in super Yang-Mills theories,” JHEP05, 015 (2003) [arXiv:hep-th/0302205 [hep-th]]

    2003 arXiv

  80. [88]

    Low-energy dynamics in N=2 super QED: Two loop approximation,

    S. M. Kuzenko and I. N. McArthur, “Low-energy dynamics in N=2 super QED: Two loop approximation,” JHEP 10, 029 (2003) [arXiv:hep-th/0308136 [hep-th]]

    2003 arXiv

  81. [89]

    Supersymmetric Euler-Heisenberg effective action: Two-loop results,

    S. M. Kuzenko and S. J. Tyler, “Supersymmetric Euler-Heisenberg effective action: Two-loop results,” JHEP 05, 081 (2007) [arXiv:hep-th/0703269 [hep-th]]

    2007 arXiv

  82. [90]

    Quantum N=3, d=3 Chern-Simons matter theories in harmonic superspace,

    I. L. Buchbinder, E. A. Ivanov, O. Lechtenfeld, N. G. Pletnev, I. B. Samsonov and B. M. Zupnik, “Quantum N=3, d=3 Chern-Simons matter theories in harmonic superspace,” JHEP 10, 075 (2009) [arXiv:0909.2970 [hep-th]]. 53

    2009 arXiv

  83. [91]

    Wess and J

    J. Wess and J. Bagger, Supersymmetry and Supergravity, Princeton University Press, Princeton, 1992

    1992

  84. [92]

    Cones, tri-Sasakian structures and superconformal invariance,

    G. W. Gibbons and P. Rychenkova, “Cones, tri-Sasakian structures and superconformal invariance,” Phys. Lett. B 443, 138 (1998) [arXiv:hep-th/9809158]. 54

    1998 arXiv

Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.