Pith. sign in

REVIEW 3 major objections 6 minor 45 references

Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

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

Pith's one-line read This paper constructs a quantizable worldsheet action for the superstring in AdS3 x S3 x T4 with mixed NS-NS and R-R three-form flux and proves one-loop conformal invariance for any flux values.

desk verdict Genuinely new manifestly supersymmetric action for mixed-flux AdS3 x S3 x T4, with one-loop conformal invariance mostly demonstrated; the omitted ghost-sector cancellation needs to be written out before the claim is fully rigorous. read the letter →

arxiv 2411.18848 v2 pith:WBBT367B submitted 2024-11-28 hep-th

Cassiano A. Daniel This is my paper · ORCID
classification hep-th MSC 81T3081T4083E30 PACS 11.25.-w11.25.Hf
keywords superstringAdS3/CFT2mixedfluxworldsheetactionPSU(11|2)purespinorformalismhybridone-loopconformalinvariance
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

The paper aims to give a covariant, quantizable worldsheet description of the type IIB superstring on $\mathrm{AdS}_3\times S^3\times T^4$ when both NS-NS and R-R three-form flux are turned on, a regime where the standard RNS and Green-Schwarz formalisms are difficult to quantize. The proposed action is built from left-invariant currents on the super-coset $\mathrm{PSU}(1,1|2)\times\mathrm{PSU}(1,1|2)/\mathrm{SO}(1,2)\times\mathrm{SO}(3)$ together with bosonic ghost variables, and keeps all sixteen spacetime supersymmetries manifest. Using a covariant background-field expansion, the paper shows that the one-loop $\beta$ function vanishes for any values of the flux parameters $f_{\mathrm{NS}}$ and $f_{\mathrm{RR}}$. If correct, this is the $\mathrm{AdS}_3\times S^3$ analogue of the pure spinor action for $\mathrm{AdS}_5\times S^5$, and gauge-fixing it recovers the known hybrid worldsheet description of the same mixed-flux background.

What carries the argument

The central object is the super-coset $\mathrm{PSU}(1,1|2)\times\mathrm{PSU}(1,1|2)/\mathrm{SO}(1,2)\times\mathrm{SO}(3)$, whose left-invariant one-forms $J^A=(g^{-1}dg)^A$ are identified with the target-space super-vielbein. The action combines a kinetic term for these currents, kinetic terms for the bosonic ghosts $\lambda^\alpha$ and $w_\alpha$ and their right-moving partners, a Wess-Zumino term built from a closed three-form $H_{\mathrm{NS}}$ proportional to $f_{\mathrm{NS}}$ and an exact term $H_{\mathrm{RR}}$ proportional to $f_{\mathrm{RR}}$, and free chiral bosons and $T^4$ fields. One-loop conformal invariance is checked by expanding $g=g_{\mathrm{cl}}e^{fX}$, where $X$ generates the quantum fluctuations; the logarithmically divergent part of the effective action vanishes using structure-constant identities and $C_2(\mathrm{PSU}(1,1|2)\times\mathrm{PSU}(1,1|2))=0$.

What would settle it

Compute the full one-loop effective action including the ghost-fluctuation diagrams that the paper sets aside as order-one, and verify that the divergent part still vanishes when both $f_{\mathrm{NS}}$ and $f_{\mathrm{RR}}$ are nonzero; alternatively, derive the omitted $\rho,\sigma$-matter couplings in (3.1) and test whether they shift the $\beta$ function.

Watch

Extended reading notes

Core claim

The central claim is that equation (3.14) of the paper is a consistent quantizable worldsheet action for the superstring on $\mathrm{AdS}_3\times S^3\times T^4$ with self-dual NS-NS and R-R three-form flux parametrized by $f_{\mathrm{NS}}$ and $f_{\mathrm{RR}}$, with total inverse radius $f=\sqrt{f_{\mathrm{NS}}^2+f_{\mathrm{RR}}^2}$. The action is manifestly invariant under $\mathrm{PSU}(1,1|2)\times\mathrm{PSU}(1,1|2)$, contains no Kappa-symmetry gauge fixing, and its one-loop effective action has no ultraviolet divergences. The order-one divergent pieces cancel because the second Casimir of $\mathrm{PSU}(1,1|2)\times\mathrm{PSU}(1,1|2)$ vanishes, while the flux-dependent pieces cancel through identities among the structure constants and the three-form components. Section 5 then shows that imposing the constraints $D_\alpha=0$ and gauge-fixing reduces the action to the hybrid formalism action for $\mathrm{AdS}_3\times S^3$ with mixed flux, providing a consistency check of the construction.

Load-bearing premise

The proof assumes that the omitted higher-order terms coupling the chiral bosons $\rho,\sigma$ to matter and ghosts do not affect the one-loop $\beta$ function, and that the bosonic ghost fluctuations contribute only order-one divergences that cancel through the vanishing second Casimir.

Editorial extensions

If this is right

  • If the construction is correct, it provides a covariant quantization of the mixed-flux $\mathrm{AdS}_3\times S^3\times T^4$ superstring with all sixteen spacetime supersymmetries manifest and no Kappa-symmetry gauge fixing.
  • It supplies a new set of worldsheet variables for vertex operators and scattering amplitudes in $\mathrm{AdS}_3$, the lower-dimensional counterpart of the pure spinor variables used for $\mathrm{AdS}_5\times S^5$.
  • In the limit $f_{\mathrm{RR}}\to 0$ the action reduces to a pure NS-NS super-coset model, giving a new description of the pure NS-NS background at unit flux where the $\mathrm{AdS}_3/\mathrm{CFT}_2$ duality is well understood.
  • One-loop conformal invariance implies that the background superfields satisfy the on-shell supergravity constraints, providing a worldsheet-level check of the mixed-flux background itself.

Reading between the lines

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

  • The paper leaves open the omitted higher-order couplings between the chiral bosons $\rho,\sigma$ and matter; if those terms contribute at one loop, the constant-deformation truncation in (3.1) would need to be extended rather than ignored.
  • The same super-coset construction with bosonic ghosts may generalize to other $\mathrm{AdS}_{d+1}\times S^{d+1}$ cosets with mixed flux, yielding a uniform covariant quantization scheme.
  • Because gauge-fixing recovers the hybrid formalism, amplitudes computed in hybrid variables could in principle be lifted to the manifestly supersymmetric variables, potentially informing the amplitude prescription in the $\mathrm{AdS}_5\times S^5$ pure spinor formalism.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 6 minor

Summary. The paper constructs a worldsheet action for the Type IIB superstring on AdS3 x S3 x T4 with mixed NS-NS and R-R three-form flux, written in terms of the PSU(1,1|2) x PSU(1,1|2) supercoset and supplemented by bosonic ghost variables (w, lambda) and their right-moving counterparts. The authors present two derivations of the action: one from background superfields satisfying supergravity constraints and one from a perturbative expansion of the massless integrated vertex operator around flat six-dimensional space. They then use the covariant background-field method to argue that the one-loop effective action has no divergent part, using the vanishing of the second Casimir of PSU(1,1|2) x PSU(1,1|2), and they show that after gauge fixing the model reduces to the Berkovits-Vafa-Witten hybrid action with mixed flux. The central claim is that the action (3.14) is quantizable, manifestly supersymmetric, and conformally invariant at one loop for arbitrary values of f_NS and f_RR.

Significance. If the one-loop conformal invariance claim is correct, the paper provides a new covariant quantization scheme for AdS3 x S3 x T4 with mixed flux in which all sixteen spacetime supersymmetries are manifest. This is a significant step for the AdS3/CFT2 correspondence and for clarifying the relation between supercoset descriptions and the hybrid formalism. The paper has several concrete strengths: the flux-dependent coefficients C^(1)_ab, C^(2)_abc and C^(3)_abc are computed explicitly and their cancellations are displayed; the relation to the hybrid formalism in Section 5 is a nontrivial cross-check; and the constructions in Sections 3.3 and 3.4 give two complementary derivations of the same action. The main caveat is that part of the one-loop proof, in particular the O(1) ghost-sector divergences, is asserted rather than computed, and the action is truncated by omitting possible higher-order couplings of the chiral bosons. These points do not appear to be fatal, but they need to be addressed before the central claim can be accepted without reservation.

major comments (3)
  1. [Section 4, after eq. (4.6) and around eq. (4.15)] The one-loop proof relies on the assertion that all O(1) divergent terms proportional to the classical fields {J[ab]J[cd], J[ab]Ncd, J[ab]Nhat_cd, NabNhat_cd} cancel through C2(PSU(1,1|2) x PSU(1,1|2)) = 0, with the ghost-loop contributions dismissed by the statement that contractions of the ghost fluctuations 'only contribute to these O(1) factors'. This is not demonstrated in the manuscript. The ghosts w,lambda are not the pure spinors of ref. [38], and their couplings to quantum fluctuations through the connection in (3.15) and through N Nhat make a ghost-loop contribution with external J^a J^b or J^a N legs a priori possible. Since ref. [38] is a ten-dimensional pure-spinor computation with different ghost content, the C2=0 argument does not automatically transfer. I request an explicit display of the ghost-dependent terms in the background-field expansion, or a direct computation showing that their one-loop divergent part is proportional to the vanishing second Casimir.
  2. [Section 3.1, eq. (3.1), and Section 4] The action (3.14) is obtained from (3.1) after truncating to constant deformations of the R-R superfield strength and related superfields, and the text explicitly states that higher-order terms coupling the chiral bosons rho,sigma to matter and ghosts will not be determined. The one-loop computation in Section 4 is performed only for the truncated action. If such higher-order terms exist and contribute at one loop, then (3.14) may not be the complete quantizable worldsheet action. Please either prove that these terms are absent by PSU(1,1|2) x PSU(1,1|2) invariance and the constant-flux assumption, or show explicitly that their inclusion cannot affect the one-loop beta function.
  3. [Section 4, eq. (4.12) and eqs. (4.13)-(4.14)] The vanishing of the one-loop divergences with two external fermionic currents is only partially exhibited. Equation (4.12) displays the J^beta-hat_k J^alpha_j terms and relegates the remaining two-fermion-current contributions to '(... )', with the statement that by symmetry they must be proportional to the combinations in eqs. (4.13)-(4.14). Since this is one of the two classes of potential one-loop divergences, the proof is complete only if these residual terms are listed or their proportionality to the vanishing combinations is shown step by step. Please provide the missing terms or a systematic enumeration of the structure-constant combinations that can appear.
minor comments (6)
  1. [Section 1] The sentence 'This paper ir organized as follows' should read 'This paper is organized as follows'.
  2. [Section 2] There are typos: 'metion' should be 'mention' and 'conventios' should be 'conventions'.
  3. [Section 3.2] The word 'ejoyed' should be 'enjoyed' in the sentence about the Z2-symmetry.
  4. [Section 4] The word 'effectve' should be 'effective'.
  5. [Section 6] The word 'containts' should be 'contains'.
  6. [Equation (3.20)] The definitions of lambda and w in the line immediately after (3.20) are difficult to parse; in particular, 'lambda_{alpha j} = 1/sqrt(2) {lambda_alpha, lambda_alpha}' appears to have an index error. Please clarify the double-index notation.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the mixed-flux action is constructed from independent supergravity/vertex-operator input, and the one-loop check is a consistency verification, not a disguised fit.

full rationale

The paper's central novelty is the action (3.14), built from left-invariant currents of PSU(1,1|2)×PSU(1,1|2) and from background superfields that are explicitly given in Section 3.3 and cross-checked in Section 3.4 by a linearized integrated-vertex computation around flat space. The background data in (3.25) come from prior independent work ([28],[19]), and the mixed-flux deformation is obtained by adding a closed Wess-Zumino three-form plus a two-form modification whose coefficient (3.32b) is stated as a consistency requirement, not as a prediction from a fitted dataset. The one-loop calculation in Section 4 is a genuine computation: it evaluates the divergent part of the effective action from the explicit fluctuation action in Appendix E, uses PSU(1,1|2)×PSU(1,1|2) identities and the f_RR^2 + f_NS^2 = f^2 relation to show C^(1),(2),(3)_abc = 0, and checks fermionic and bosonic sectors separately. The only unproved sub-step — the O(1) ghost-sector cancellation attributed to refs. [27,38] via C2 = 0 — is a proof gap, not circularity, because it imports a prior computation as evidence rather than defining the target quantity in terms of itself. The self-citation [16] supplies the flat-space hybrid formalism and integrated vertex operator, but the AdS3 mixed-flux action and its one-loop finiteness are not assumed there; they are the new result. The gauge-fixing relation to the BVW action in Section 5 is an independent consistency check in the other direction. No step reduces to 'X is true because we defined X'.

Assumptions & free parameters 2 free parameters · 5 assumptions · 1 invented entities

The construction rests on the supercoset description of AdS3 x S3, on the pure-RR background superfields from the prior literature, and on the validity of the background field method for this model. The most delicate input is the truncated coupling to the rho,sigma ghosts, which the paper does not determine.

free parameters (2)
  • Coefficient in the two-form potential B_{alpha j beta k} = (2 - f_RR/f)/4
    The relative coefficient in B is chosen so that the one-loop beta function vanishes (Section 4) and the pure R-R action is recovered in the f_NS to 0 limit; it is fixed by consistency rather than derived from an independent principle.
  • Flux parameters f_NS and f_RR
    Physical background parameters, inputs from supergravity, not fitted to data. They parametrize the NS-NS and R-R three-form fluxes, with f = sqrt(f_NS^2 + f_RR^2).
assumptions (5)
  • domain assumption The supercoset PSU(1,1|2) x PSU(1,1|2) / (SO(1,2) x SO(3)) with structure constants (3.7) and Z4 grading describes the AdS3 x S3 target superspace.
    Used throughout Section 3 to identify the left-invariant currents with the super-vielbein and to write the action.
  • domain assumption The pure R-R background superfields (3.25) satisfy the supergravity torsion constraints (3.26) and curvature relations, as derived in refs. [28,19].
    Provides the starting point for the pure R-R action (3.29) and the subsequent mixed-flux deformation.
  • domain assumption The covariant background field method with the ghost propagator (4.8) is valid, and O(1) divergences cancel via C2(PSU(1,1|2)xPSU(1,1|2)) = 0.
    Borrowed from the AdS5 pure spinor computation [38]; the paper verifies the relevant Casimir vanishes but does not re-derive the method.
  • ad hoc to paper Higher-order terms in the R-R superfield strength F_{alpha j beta k} that couple the rho,sigma ghosts to matter are absent or can be ignored for worldsheet consistency.
    Explicitly stated in Section 3.1 ('We will not be concerned in determining them'); this truncation is assumed to give a consistent action.
  • ad hoc to paper The unconstrained bosonic ghosts {lambda, w} with OPE (2.2c) provide a consistent quantization without adding non-minimal variables.
    The paper states that non-minimal variables are not necessary for understanding the allowed deformations; this is an assumption about the quantum measure.
invented entities (1)
  • Unconstrained bosonic worldsheet ghosts (lambda_alpha, w_alpha, lambda-hat, w-hat)
    purpose: Maintain manifest PSU(1,1|2) x PSU(1,1|2) supersymmetry in the curved background action, playing the role of pure spinor variables.
    These are formal worldsheet degrees of freedom adopted from the extended hybrid formalism [16]; they have no direct physical observable and their consistency is assessed only through conformal invariance.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux." pith.science (2026). https://pith.science/paper/WBBT367B

@misc{pith2026241118848,
  author       = {Pith},
  title        = {Pith review of: Covariant quantization of the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed flux},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WBBT367B}},
  note         = {Machine review of arXiv:2411.18848}
}
abstract

A quantizable and manifestly $\text{PSU}(1,1|2) \times \text{PSU}(1,1|2)$-invariant action for the superstring in $\rm AdS_3 \times S^3 \times T^4$ with mixed NS-NS and R-R self-dual three-form flux is constructed, which is the analogue of the $\rm AdS_5 \times S^ 5$ pure spinor action for $\rm AdS_3 \times S^3$. The model is then quantized and proven to be conformal invariant at the one-loop level. We conclude by showing how one can relate the supersymmetric description with the Berkovits-Vafa-Witten $\rm AdS_3 \times S^3$ worldsheet action with mixed flux.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

45 extracted references · 18 canonical work pages

  1. [38]

    One Loop Conformal Invariance of the Superstring in an AdS_5 x S^5 Background

    B.C. Vallilo,One loop conformal invariance of the superstring in an AdS(5) x S5 background, JHEP 12 (2002) 042 [hep-th/0210064]

    work page Pith review arXiv 2002

  2. [1]

    Maldacena,The Large N limit of superconformal field theories and supergravity, Adv

    J.M. Maldacena,The Large N limit of superconformal field theories and supergravity, Adv. Theor. Math. Phys.2 (1998) 231 [hep-th/9711200]

    arXiv 1998

  3. [2]

    Quantization of the Superstring in Ramond-Ramond Backgrounds

    N. Berkovits,Quantization of the superstring in Ramond-Ramond backgrounds, Class. Quant. Grav.17 (2000) 971 [hep-th/9910251]

    work page Pith review arXiv 2000

  4. [3]

    Metsaev and A.A

    R.R. Metsaev and A.A. Tseytlin,Type IIB superstring action in AdS(5) x S**5 background, Nucl. Phys. B533 (1998) 109 [hep-th/9805028]

    arXiv 1998

  5. [4]

    Light-Cone Gauge Quantization of 2D Sigma Models

    R.E. Rudd,Light cone gauge quantization of 2-D sigma models, Nucl. Phys. B427 (1994) 81 [hep-th/9402106]

    work page Pith review arXiv 1994

  6. [5]

    Superstring action in AdS_5 x S^5: kappa symmetry light cone gauge

    R.R. Metsaev and A.A. Tseytlin,Superstring action in AdS(5) x S**5. Kappa symmetry light cone gauge, Phys. Rev. D63 (2001) 046002 [hep-th/0007036]. – 41 –

    work page Pith review arXiv 2001

  7. [6]

    Maldacena and H

    J.M. Maldacena and H. Ooguri,Strings in AdS(3) and SL(2,R) WZW model 1.: The Spectrum, J. Math. Phys.42 (2001) 2929 [hep-th/0001053]

    arXiv 2001

  8. [7]

    M. Cho, S. Collier and X. Yin,Strings in Ramond-Ramond Backgrounds from the Neveu-Schwarz-Ramond Formalism, JHEP 12 (2020) 123 [1811.00032]

    arXiv 2020

Show all 45 references
  1. [8]

    Gaberdiel and R

    M.R. Gaberdiel and R. Gopakumar,Tensionless string spectra on AdS3, JHEP 05 (2018) 085 [1803.04423]

    2018 arXiv

  2. [9]

    Eberhardt, M.R

    L. Eberhardt, M.R. Gaberdiel and R. Gopakumar,The Worldsheet Dual of the Symmetric Product CFT, JHEP 04 (2019) 103 [1812.01007]

    2019 arXiv

  3. [10]

    Berkovits, C

    N. Berkovits, C. Vafa and E. Witten,Conformal field theory of AdS background with Ramond-Ramond flux, JHEP 03 (1999) 018 [hep-th/9902098]

    1999 arXiv

  4. [11]

    Daniel,Integrating out the fermions in AdS, 2408.10418

    C.A. Daniel,Integrating out the fermions in AdS, 2408.10418

    arXiv

  5. [12]

    Eberhardt, M.R

    L. Eberhardt, M.R. Gaberdiel and R. Gopakumar,Deriving the AdS3/CFT2 correspondence, JHEP 02 (2020) 136 [1911.00378]

    2020 arXiv

  6. [13]

    Dei, M.R

    A. Dei, M.R. Gaberdiel, R. Gopakumar and B. Knighton,Free field world-sheet correlators for AdS3, JHEP 02 (2021) 081 [2009.11306]

    2021 arXiv

  7. [14]

    Gaberdiel, R

    M.R. Gaberdiel, R. Gopakumar and B. Nairz,Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold, 2312.13288

    arXiv

  8. [15]

    A. Dei, B. Knighton and K. Naderi,Solving AdS3 string theory at minimal tension: tree-level correlators, 2312.04622

    arXiv

  9. [16]

    Daniel,Vertex operators for the superstring with manifestd = 6N = 1 supersymmetry, 2412.06194

    C.A. Daniel,Vertex operators for the superstring with manifestd = 6N = 1 supersymmetry, 2412.06194

    arXiv

  10. [17]

    Bedoya and O

    O.A. Bedoya and O. Chandia,One-loop Conformal Invariance of the Type II Pure Spinor Superstring in a Curved Background, JHEP 01 (2007) 042 [hep-th/0609161]

    2007 arXiv

  11. [18]

    Berkovits and C

    N. Berkovits and C. Vafa,N=4 topological strings, Nucl. Phys. B433 (1995) 123 [hep-th/9407190]

    1995 arXiv

  12. [19]

    Berkovits,Super Poincare covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035]

    N. Berkovits,Super Poincare covariant quantization of the superstring, JHEP 04 (2000) 018 [hep-th/0001035]

    2000 arXiv

  13. [20]

    Gerigk and I

    S. Gerigk and I. Kirsch,On the Relation between Hybrid and Pure Spinor String Theory, JHEP 03 (2010) 106 [0912.2347]

    2010 arXiv

  14. [21]

    Berkovits,Quantum consistency of the superstring in AdS(5) x S**5 background, JHEP 03 (2005) 041 [hep-th/0411170]

    N. Berkovits,Quantum consistency of the superstring in AdS(5) x S**5 background, JHEP 03 (2005) 041 [hep-th/0411170]

    2005 arXiv

  15. [22]

    Dolan and E

    L. Dolan and E. Witten,Vertex operators for AdS(3) background with Ramond-Ramond flux, JHEP 11 (1999) 003 [hep-th/9910205]

    1999 arXiv

  16. [23]

    Bobkov and L

    K. Bobkov and L. Dolan,Three graviton amplitude in Berkovits-Vafa-Witten variables, Phys. Lett. B537 (2002) 155 [hep-th/0201027]

    2002 arXiv

  17. [24]

    Berkovits,Sketching a Proof of the Maldacena Conjecture at Small Radius, JHEP 06 (2019) 111 [1903.08264]

    N. Berkovits,Sketching a Proof of the Maldacena Conjecture at Small Radius, JHEP 06 (2019) 111 [1903.08264]. – 42 –

    2019 arXiv

  18. [25]

    Cagnazzo and K

    A. Cagnazzo and K. Zarembo,B-field in AdS(3)/CFT(2) Correspondence and Integrability, JHEP 11 (2012) 133 [1209.4049]

    2012 arXiv

  19. [26]

    Babichenko, A

    A. Babichenko, A. Dekel and O. Ohlsson Sax,Finite-gap equations for strings on AdS3 x S3 x T4 with mixed 3-form flux, JHEP 11 (2014) 122 [1405.6087]

    2014 arXiv

  20. [27]

    Berkovits, M

    N. Berkovits, M. Bershadsky, T. Hauer, S. Zhukov and B. Zwiebach,Superstring theory on AdS(2) x S**2 as a coset supermanifold, Nucl. Phys. B567 (2000) 61 [hep-th/9907200]

    2000 arXiv

  21. [28]

    Berkovits,Quantization of the type II superstring in a curved six-dimensional background, Nucl

    N. Berkovits,Quantization of the type II superstring in a curved six-dimensional background, Nucl. Phys. B565 (2000) 333 [hep-th/9908041]

    2000 arXiv

  22. [29]

    Benichou,First-principles derivation of the AdS/CFT Y-systems, JHEP 10 (2011) 112 [1108.4927]

    R. Benichou,First-principles derivation of the AdS/CFT Y-systems, JHEP 10 (2011) 112 [1108.4927]

    2011 arXiv

  23. [30]

    Berkovits and P.S

    N. Berkovits and P.S. Howe,Ten-dimensional supergravity constraints from the pure spinor formalism for the superstring, Nucl. Phys. B635 (2002) 75 [hep-th/0112160]

    2002 arXiv

  24. [31]

    Wess and J

    J. Wess and J. Bagger,Supersymmetry and supergravity, Princeton University Press (1992)

    1992

  25. [32]

    Berkovits,A New Limit of the AdS(5) x S**5 Sigma Model, JHEP 08 (2007) 011 [hep-th/0703282]

    N. Berkovits,A New Limit of the AdS(5) x S**5 Sigma Model, JHEP 08 (2007) 011 [hep-th/0703282]

    2007 arXiv

  26. [33]

    Pesando,The GS type IIB superstring action on AdS(3) x S(3) x T**4, JHEP 02 (1999) 007 [hep-th/9809145]

    I. Pesando,The GS type IIB superstring action on AdS(3) x S(3) x T**4, JHEP 02 (1999) 007 [hep-th/9809145]

    1999 arXiv

  27. [34]

    Rahmfeld and A

    J. Rahmfeld and A. Rajaraman,The GS string action on AdS(3) x S(3) with Ramond-Ramond charge, Phys. Rev. D60 (1999) 064014 [hep-th/9809164]

    1999 arXiv

  28. [35]

    Park and S.-J

    J. Park and S.-J. Rey,Green-Schwarz superstring on AdS(3) x S**3, JHEP 01 (1999) 001 [hep-th/9812062]

    1999 arXiv

  29. [36]

    Berkovits and O

    N. Berkovits and O. Chandia,Superstring vertex operators in an AdS(5) x S**5 background, Nucl. Phys. B596 (2001) 185 [hep-th/0009168]

    2001 arXiv

  30. [37]

    de Boer and K

    J. de Boer and K. Skenderis,Covariant computation of the low-energy effective action of the heterotic superstring, Nucl. Phys. B481 (1996) 129 [hep-th/9608078]

    1996 arXiv

  31. [39]

    Mazzucato,Superstrings in AdS, Phys

    L. Mazzucato,Superstrings in AdS, Phys. Rept. 521 (2012) 1 [1104.2604]

    2012 arXiv

  32. [40]

    de Wit, M.T

    B. de Wit, M.T. Grisaru and P. van Nieuwenhuizen,The WZNW model at two loops, Nucl. Phys. B408 (1993) 299 [hep-th/9307027]

    1993 arXiv

  33. [41]

    Berkovits,Half-BPS vertex operators of the AdS5× S5 superstring, JHEP 07 (2019) 084 [1904.06564]

    N. Berkovits,Half-BPS vertex operators of the AdS5× S5 superstring, JHEP 07 (2019) 084 [1904.06564]

    2019 arXiv

  34. [42]

    Fleury and L.N.S

    T. Fleury and L.N.S. Martins,AdS5 × S5 supergravity vertex operators, JHEP 07 (2021) 210 [2104.03333]. – 43 –

    2021 arXiv

  35. [43]

    Berkovits,Simplifying and Extending the AdS(5) x S**5 Pure Spinor Formalism, JHEP 09 (2009) 051 [0812.5074]

    N. Berkovits,Simplifying and Extending the AdS(5) x S**5 Pure Spinor Formalism, JHEP 09 (2009) 051 [0812.5074]

    2009 arXiv

  36. [44]

    Gaberdiel and R

    M.R. Gaberdiel and R. Gopakumar,The worldsheet dual of free super Yang-Mills in 4D, JHEP 11 (2021) 129 [2105.10496]

    2021 arXiv

  37. [45]

    Vallilo,Flat currents in the classical AdS(5) x S**5 pure spinor superstring, JHEP 03 (2004) 037 [hep-th/0307018]

    B.C. Vallilo,Flat currents in the classical AdS(5) x S**5 pure spinor superstring, JHEP 03 (2004) 037 [hep-th/0307018]. – 44 –

    2004 arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.