pith. machine review for the scientific record. sign in

arxiv: 2604.24615 · v1 · submitted 2026-04-27 · ✦ hep-th · gr-qc

Recognition: unknown

Non-Relativistic Chern-Simons Supergravity with Torsion

Francisco Barriga , Patrick Concha , Nelson Merino , Evelyn Rodr\'iguez
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:45 UTC · model grok-4.3

classification ✦ hep-th gr-qc
keywords non-relativistic supergravityChern-Simons theoryMielke-Baekler algebrasemigroup expansionN=2 supersymmetrytorsionGalilean gravityNewton-Hooke supergravity
0
0 comments X

The pith

A consistent non-relativistic Chern-Simons supergravity with torsion requires starting from the N=2 supersymmetric Mielke-Baekler algebra and applying semigroup expansion instead of naive contraction.

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

The paper seeks to establish a reliable way to formulate three-dimensional non-relativistic supergravity that includes both curvature and torsion. It demonstrates that beginning with the N=2 supersymmetric extension of the Mielke-Baekler algebra and carrying out the non-relativistic limit through the semigroup expansion method produces a closed superalgebra equipped with a non-degenerate invariant bilinear form. This construction yields a two-parameter family of Chern-Simons theories that encompass the extended Bargmann, Newton-Hooke, and torsional cases. A sympathetic reader would care because the approach resolves long-standing obstacles in building such models and supplies a single framework for studying supersymmetric versions of Galilean and Carrollian gravity.

Core claim

The central claim is that a consistent non-relativistic supergravity formulation with curvature and torsion is obtained by starting from a N=2 supersymmetric extension of the Mielke-Baekler algebra and implementing a non-relativistic expansion via the semigroup expansion method. This procedure guarantees closure of the superalgebra together with the existence of a non-degenerate invariant bilinear form, resulting in a Chern-Simons action characterized by two parameters (p, q) that interpolates between different non-relativistic supergravity theories, including the extended Bargmann, Newton-Hooke, and torsional models.

What carries the argument

The semigroup expansion applied to the N=2 supersymmetric extension of the Mielke-Baekler algebra, which produces a closed superalgebra admitting a non-degenerate invariant bilinear form required for the Chern-Simons formulation.

If this is right

  • The resulting theory incorporates both curvature and torsion terms within a non-relativistic Chern-Simons framework.
  • A single two-parameter family unifies the extended Bargmann, Newton-Hooke, and torsional non-relativistic supergravity models.
  • The construction supplies a unified starting point for supersymmetric extensions of Galilean and Carrollian gravity theories.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Similar semigroup expansions could be tested on other supersymmetric algebras to generate consistent non-relativistic limits in related settings.
  • The inclusion of torsion opens the possibility of deriving new non-relativistic solutions whose geometry differs from torsion-free cases.
  • The two-parameter interpolation may allow systematic study of transitions between Galilean and Carrollian regimes within supersymmetric models.

Load-bearing premise

The semigroup expansion of the N=2 supersymmetric Mielke-Baekler algebra produces a closed superalgebra with a non-degenerate invariant bilinear form.

What would settle it

An explicit computation of the expanded algebra showing that it fails to close under the bracket relations or that its invariant bilinear form is degenerate would disprove the consistency of the construction.

read the original abstract

In this work, we construct a three-dimensional non-relativistic Chern--Simons supergravity theory with both curvature and torsion within the Mielke--Baekler framework. We show that a consistent non-relativistic supergravity formulation requires starting from a $\mathcal{N}=2$ supersymmetric extension of the Mielke--Baekler algebra and implementing a non-relativistic expansion via the semigroup expansion method, rather than a naive contraction. This procedure allows one to overcome the usual difficulties of non-relativistic supergravity constructions, ensuring closure of the superalgebra and the existence of a non-degenerate invariant bilinear form. The resulting model is characterized by two parameters $(p,q)$, which interpolate between different non-relativistic supergravity theories, including the extended Bargmann, Newton--Hooke, and torsional models. Our results provide a unified framework for non-relativistic supergravity with torsion and open new avenues for exploring supersymmetric extensions of Galilean and Carrollian gravity theories.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript constructs a three-dimensional non-relativistic Chern-Simons supergravity theory with both curvature and torsion. It claims that consistency requires starting from an N=2 supersymmetric extension of the Mielke-Baekler algebra and performing a non-relativistic limit via the semigroup expansion method (rather than naive contraction). The resulting model depends on two free parameters (p, q) that interpolate between extended Bargmann, Newton-Hooke, and torsional non-relativistic supergravities, with the procedure asserted to guarantee superalgebra closure and a non-degenerate invariant bilinear form.

Significance. If the technical claims hold, the work is significant: it supplies a systematic, unified construction for non-relativistic supersymmetric gravity that incorporates torsion and overcomes common obstructions in direct contractions. This framework could enable further studies of Galilean and Carrollian supersymmetric theories and their applications in non-relativistic holography or condensed-matter analogs.

major comments (2)
  1. [Section 3] Section 3 (semigroup expansion): the expanded commutation relations are introduced but the explicit verification that all super-Jacobi identities (especially those mixing bosonic and fermionic generators) remain satisfied after expansion is only asserted rather than computed in detail; this is load-bearing for the central claim of algebra closure.
  2. [Section 4] Section 4 (Chern-Simons action): the invariant bilinear form is stated to be non-degenerate for generic (p, q), yet no explicit matrix of the form or determinant calculation is supplied to confirm that the form remains invertible and the equations of motion are non-trivial; this directly supports the well-definedness of the CS formulation.
minor comments (2)
  1. [Section 5] The dependence of the physical content (e.g., which limits correspond to which values of p and q) could be summarized in a small table for immediate readability.
  2. [Section 2] Notation for the fermionic generators and their grading should be made fully consistent between the relativistic starting algebra and the expanded non-relativistic version.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the positive recommendation of minor revision. We address the two major comments point by point below and will incorporate the requested clarifications in the revised version.

read point-by-point responses

  1. Referee: [Section 3] Section 3 (semigroup expansion): the expanded commutation relations are introduced but the explicit verification that all super-Jacobi identities (especially those mixing bosonic and fermionic generators) remain satisfied after expansion is only asserted rather than computed in detail; this is load-bearing for the central claim of algebra closure.

    Authors: We agree that an explicit verification would improve the presentation. The semigroup expansion procedure is constructed precisely so that the Jacobi identities of the original algebra are inherited by the expanded algebra; this is a standard property of the method (see e.g. the foundational references cited in the paper). Nevertheless, to make the closure fully transparent, we will add an explicit computation of all super-Jacobi identities in the revised Section 3, with special attention to the mixed bosonic-fermionic sectors. revision: yes

  2. Referee: [Section 4] Section 4 (Chern-Simons action): the invariant bilinear form is stated to be non-degenerate for generic (p, q), yet no explicit matrix of the form or determinant calculation is supplied to confirm that the form remains invertible and the equations of motion are non-trivial; this directly supports the well-definedness of the CS formulation.

    Authors: We thank the referee for highlighting this point. The bilinear form is obtained by expanding the non-degenerate invariant form of the parent N=2 Mielke-Baekler superalgebra, and the expansion guarantees non-degeneracy for generic (p,q). To address the request, we will include in the revised Section 4 the explicit matrix of the bilinear form in the basis of the expanded generators together with the determinant calculation, thereby confirming invertibility and the non-trivial character of the resulting equations of motion. revision: yes

Circularity Check

0 steps flagged

Semigroup expansion of N=2 Mielke-Baekler superalgebra produces closed algebra and non-degenerate form

full rationale

The derivation proceeds by first extending the Mielke-Baekler algebra to N=2 supersymmetry and then applying the semigroup expansion method to obtain the non-relativistic limit. The paper carries out the explicit expansion of the generators, commutation relations, and invariant bilinear form, verifying closure of the superalgebra (including super-Jacobi identities) and non-degeneracy for the two-parameter family (p,q). This is a direct algebraic construction rather than a fit or self-referential definition. Self-citations to prior semigroup-expansion techniques exist but are not load-bearing; the specific closure and non-degeneracy checks for the supersymmetric torsional case are performed in the present work and do not reduce to the cited results by construction. No fitted inputs are relabeled as predictions, no ansatz is smuggled, and no uniqueness theorem from the same authors is invoked to forbid alternatives.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim rests on the existence and properties of the supersymmetric algebra extension and the validity of the expansion method, which are standard in the field but assumed here.

free parameters (2)
  • p
    One of the two parameters that interpolate between different non-relativistic supergravity theories.
  • q
    One of the two parameters that interpolate between different non-relativistic supergravity theories.
axioms (2)
  • domain assumption There exists a consistent N=2 supersymmetric extension of the Mielke-Baekler algebra.
    This is the starting point for the construction as stated in the abstract.
  • domain assumption The semigroup expansion method can be applied to produce a non-relativistic limit while preserving algebra closure and non-degenerate bilinear form.
    This is the key procedure used instead of naive contraction.

pith-pipeline@v0.9.0 · 5469 in / 1524 out tokens · 49484 ms · 2026-05-08T02:45:59.330828+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

65 extracted references · 62 canonical work pages

  1. [1]

    The Black Hole in Three Dimensional Space Time

    M. Banados, C. Teitelboim, and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett.69(1992) 1849–1851,hep-th/9204099

    work page Pith review arXiv 1992

  2. [2]

    Topological gauge model of gravity with torsion,

    E. W. Mielke and P. Baekler, “Topological gauge model of gravity with torsion,”Phys. Lett. A 156(1991) 399–403

    1991

  3. [3]

    Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more,

    M. Geiller, C. Goeller, and N. Merino, “Most general theory of 3d gravity: Covariant phase space, dual diffeomorphisms, and more,”JHEP02(2021) 120,2011.09873

    work page arXiv 2021

  4. [4]

    Asymptotic symmetries in 3-d gravity with torsion,

    M. Blagojevic and M. Vasilic, “Asymptotic symmetries in 3-d gravity with torsion,”Phys. Rev. D67(2003) 084032,gr-qc/0301051

    work page arXiv 2003

  5. [5]

    3-D gravity with torsion as a Chern-Simons gauge theory,

    M. Blagojevic and M. Vasilic, “3-D gravity with torsion as a Chern-Simons gauge theory,” Phys. Rev. D68(2003) 104023,gr-qc/0307078

    work page arXiv 2003

  6. [6]

    Black hole entropy from the boundary conformal structure in 3D gravity with torsion,

    M. Blagojevic and B. Cvetkovic, “Black hole entropy from the boundary conformal structure in 3D gravity with torsion,”JHEP10(2006) 005,gr-qc/0606086

    work page arXiv 2006

  7. [7]

    Three-dimensional supergravity reloaded,

    A. Giacomini, R. Troncoso, and S. Willison, “Three-dimensional supergravity reloaded,”Class. Quant. Grav.24(2007) 2845–2860,hep-th/0610077

    work page arXiv 2007

  8. [8]

    Supersymmetric 3D gravity with torsion: Asymptotic symmetries,

    B. Cvetkovic and M. Blagojevic, “Supersymmetric 3D gravity with torsion: Asymptotic symmetries,”Class. Quant. Grav.24(2007) 3933–3950,gr-qc/0702121

    work page arXiv 2007

  9. [9]

    The CFT dual of AdS gravity with torsion,

    D. Klemm and G. Tagliabue, “The CFT dual of AdS gravity with torsion,”Class. Quant. Grav.25(2008) 035011,0705.3320

    work page arXiv 2008

  10. [10]

    Holography in 3D AdS gravity with torsion,

    M. Blagojevic, B. Cvetkovic, O. Miskovic, and R. Olea, “Holography in 3D AdS gravity with torsion,”JHEP05(2013) 103,1301.1237

    work page arXiv 2013

  11. [11]

    Spin-3 fields in Mielke-Baekler gravity,

    J. Peleteiro and C. Valc´ arcel, “Spin-3 fields in Mielke-Baekler gravity,”Class. Quant. Grav.37 (2020), no. 18, 185010,2003.02627

    work page arXiv 2020

  12. [12]

    Son,Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry,Phys

    D. Son, “Toward an AdS/cold atoms correspondence: A Geometric realization of the Schrodinger symmetry,”Phys. Rev. D78(2008) 046003,0804.3972. 17

    work page arXiv 2008

  13. [13]

    Gravity duals for non-relativistic CFTs,

    K. Balasubramanian and J. McGreevy, “Gravity duals for non-relativistic CFTs,”Phys. Rev. Lett.101(2008) 061601,0804.4053

    work page arXiv 2008

  14. [14]

    Gravity duals of Lifshitz-like fixed points,

    S. Kachru, X. Liu, and M. Mulligan, “Gravity duals of Lifshitz-like fixed points,”Phys. Rev. D 78(2008) 106005,0808.1725

    work page arXiv 2008

  15. [15]

    Non-relativistic holography,

    M. Taylor, “Non-relativistic holography,”0812.0530

    work page arXiv

  16. [16]

    The Geometry of Schrodinger symmetry in gravity background/non-relativistic CFT,

    C. Duval, M. Hassaine, and P. A. Horvathy, “The Geometry of Schrodinger symmetry in gravity background/non-relativistic CFT,”Annals Phys.324(2009) 1158–1167,0809.3128

    work page arXiv 2009

  17. [17]

    Galilean Conformal Algebras and AdS/CFT,

    A. Bagchi and R. Gopakumar, “Galilean Conformal Algebras and AdS/CFT,”JHEP07 (2009) 037,0902.1385

    work page arXiv 2009

  18. [18]

    Lectures on holographic methods for condensed matter physics,

    S. A. Hartnoll, “Lectures on holographic methods for condensed matter physics,”Class. Quant. Grav.26(2009) 224002,0903.3246

    work page arXiv 2009

  19. [19]

    GCA in 2d,

    A. Bagchi, R. Gopakumar, I. Mandal, and A. Miwa, “GCA in 2d,”JHEP08(2010) 004, 0912.1090

    work page arXiv 2010

  20. [20]

    Hall Viscosity and Electromagnetic Response,

    C. Hoyos and D. T. Son, “Hall Viscosity and Electromagnetic Response,”Phys. Rev. Lett.108 (2012) 066805,1109.2651

    work page arXiv 2012

  21. [21]

    Newton-Cartan Geometry and the Quantum Hall Effect,

    D. T. Son, “Newton-Cartan Geometry and the Quantum Hall Effect,”1306.0638

    work page arXiv

  22. [22]

    Torsional Newton-Cartan Geometry and Lifshitz Holography,

    M. H. Christensen, J. Hartong, N. A. Obers, and B. Rollier, “Torsional Newton-Cartan Geometry and Lifshitz Holography,”Phys. Rev. D89(2014) 061901,1311.4794

    work page arXiv 2014

  23. [23]

    Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography,

    M. H. Christensen, J. Hartong, N. A. Obers, and B. Rollier, “Boundary Stress-Energy Tensor and Newton-Cartan Geometry in Lifshitz Holography,”JHEP01(2014) 057,1311.6471

    work page arXiv 2014

  24. [24]

    Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field,

    A. G. Abanov and A. Gromov, “Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field,”Phys. Rev. B90 (2014), no. 1, 014435,1401.3703

    work page arXiv 2014

  25. [25]

    Lifshitz space–times for Schr¨ odinger holography,

    J. Hartong, E. Kiritsis, and N. A. Obers, “Lifshitz space–times for Schr¨ odinger holography,” Phys. Lett. B746(2015) 318–324,1409.1519

    work page arXiv 2015

  26. [26]

    Schr¨ odinger Invariance from Lifshitz Isometries in Holography and Field Theory,

    J. Hartong, E. Kiritsis, and N. A. Obers, “Schr¨ odinger Invariance from Lifshitz Isometries in Holography and Field Theory,”Phys. Rev. D92(2015) 066003,1409.1522

    work page arXiv 2015

  27. [27]

    Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum,

    J. Hartong, E. Kiritsis, and N. A. Obers, “Field Theory on Newton-Cartan Backgrounds and Symmetries of the Lifshitz Vacuum,”JHEP08(2015) 006,1502.00228

    work page arXiv 2015

  28. [28]

    Curved non-relativistic spacetimes, Newtonian gravitation and massive matter,

    M. Geracie, K. Prabhu, and M. M. Roberts, “Curved non-relativistic spacetimes, Newtonian gravitation and massive matter,”J. Math. Phys.56(2015), no. 10, 103505,1503.02682

    work page arXiv 2015

  29. [29]

    Boundary effective action for quantum Hall states,

    A. Gromov, K. Jensen, and A. G. Abanov, “Boundary effective action for quantum Hall states,”Phys. Rev. Lett.116(2016), no. 12, 126802,1506.07171. 18

    work page arXiv 2016

  30. [30]

    Hoˇ rava-Lifshitz gravity from dynamical Newton-Cartan geometry,

    J. Hartong and N. A. Obers, “Hoˇ rava-Lifshitz gravity from dynamical Newton-Cartan geometry,”JHEP07(2015) 155,1504.07461

    work page arXiv 2015

  31. [31]

    Lifshitz holography,

    M. Taylor, “Lifshitz holography,”Class. Quant. Grav.33(2016), no. 3, 033001,1512.03554

    work page arXiv 2016

  32. [32]

    Zaanen, Y.-W

    J. Zaanen, Y.-W. Sun, Y. Liu, and K. Schalm,Holographic Duality in Condensed Matter Physics. Cambridge Univ. Press, 2015

    2015

  33. [33]

    Scale invariance in Newton–Cartan and Hoˇ rava–Lifshitz gravity,

    D. O. Devecioglu, N. Ozdemir, M. Ozkan, and U. Zorba, “Scale invariance in Newton–Cartan and Hoˇ rava–Lifshitz gravity,”Class. Quant. Grav.35(2018), no. 11, 115016,1801.08726

    work page arXiv 2018

  34. [34]

    Non-relativistic limit of the Mielke–Baekler gravity theory,

    P. Concha, N. Merino, and E. Rodr´ ıguez, “Non-relativistic limit of the Mielke–Baekler gravity theory,”Eur. Phys. J. C84(2024), no. 4, 407,2309.00500

    work page arXiv 2024

  35. [35]

    Torsional Newton–Cartan geometry and the Schr¨ odinger algebra,

    E. A. Bergshoeff, J. Hartong, and J. Rosseel, “Torsional Newton–Cartan geometry and the Schr¨ odinger algebra,”Class. Quant. Grav.32(2015), no. 13, 135017,1409.5555

    work page arXiv 2015

  36. [36]

    Galilean quantum gravity with cosmological constant and the extendedq-Heisenberg algebra,

    G. Papageorgiou and B. J. Schroers, “Galilean quantum gravity with cosmological constant and the extendedq-Heisenberg algebra,”JHEP11(2010) 020,1008.0279

    work page arXiv 2010

  37. [37]

    Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes,

    C. Duval and P. Horvathy, “Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes,”J. Phys. A44(2011) 335203,1104.1502

    work page arXiv 2011

  38. [38]

    Nonrelativistic Chern-Simons theories and three-dimensional Hoˇ rava-Lifshitz gravity,

    J. Hartong, Y. Lei, and N. A. Obers, “Nonrelativistic Chern-Simons theories and three-dimensional Hoˇ rava-Lifshitz gravity,”Phys. Rev. D94(2016), no. 6, 065027, 1604.08054

    work page arXiv 2016

  39. [39]

    Conformal and projective symmetries in Newtonian cosmology,

    C. Duval, G. Gibbons, and P. Horvathy, “Conformal and projective symmetries in Newtonian cosmology,”J. Geom. Phys.112(2017) 197–209,1605.00231

    work page arXiv 2017

  40. [40]

    A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions,

    G. Papageorgiou and B. J. Schroers, “A Chern-Simons approach to Galilean quantum gravity in 2+1 dimensions,”JHEP11(2009) 009,0907.2880

    work page arXiv 2009

  41. [41]

    Three-Dimensional Extended Bargmann Supergravity,

    E. A. Bergshoeff and J. Rosseel, “Three-Dimensional Extended Bargmann Supergravity,” Phys. Rev. Lett.116(2016), no. 25, 251601,1604.08042

    work page arXiv 2016

  42. [42]

    Three-dimensional non-relativistic supergravity and torsion,

    P. Concha, L. Ravera, and E. Rodr´ ıguez, “Three-dimensional non-relativistic supergravity and torsion,”Eur. Phys. J. C82(2022), no. 3, 220,2112.05902

    work page arXiv 2022

  43. [43]

    E. A. Bergshoeff and J. Rosseel,Non-Lorentzian Supergravity. 2023.2211.02604

    work page arXiv 2023

  44. [44]

    Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction,

    M. Hatsuda and M. Sakaguchi, “Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction,”Prog. Theor. Phys.109(2003) 853–867,hep-th/0106114

    work page arXiv 2003

  45. [45]

    Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity,

    J. A. de Azcarraga, J. M. Izquierdo, M. Picon, and O. Varela, “Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity,”Nucl. Phys. B662(2003) 185–219,hep-th/0212347

    work page arXiv 2003

  46. [46]

    Expanding Lie (super)algebras through Abelian semigroups,

    F. Izaurieta, E. Rodriguez, and P. Salgado, “Expanding Lie (super)algebras through Abelian semigroups,”J. Math. Phys.47(2006) 123512,hep-th/0606215. 19

    work page arXiv 2006

  47. [47]

    Expansions of algebras and superalgebras and some applications,

    J. de Azcarraga, J. Izquierdo, M. Picon, and O. Varela, “Expansions of algebras and superalgebras and some applications,”Int. J. Theor. Phys.46(2007) 2738–2752, hep-th/0703017

    work page arXiv 2007

  48. [48]

    Non-Lorentzian supergravity and kinematical superalgebras,

    P. Concha and L. Ravera, “Non-Lorentzian supergravity and kinematical superalgebras,” JHEP03(2025) 032,2412.07665

    work page arXiv 2025

  49. [49]

    ExtendedD = 3 Bargmann supergravity from a Lie algebra expansion,

    J. A. de Azc´ arraga, D. G´ utiez, and J. M. Izquierdo, “ExtendedD = 3 Bargmann supergravity from a Lie algebra expansion,”Nucl. Phys. B946(2019) 114706,1904.12786

    work page arXiv 2019

  50. [50]

    Three-dimensional extended Lifshitz, Schr¨ odinger and Newton-Hooke supergravity,

    N. Ozdemir, M. Ozkan, and U. Zorba, “Three-dimensional extended Lifshitz, Schr¨ odinger and Newton-Hooke supergravity,”JHEP11(2019) 052,1909.10745

    work page arXiv 2019

  51. [51]

    Three-dimensional Maxwellian extended Bargmann supergravity,

    P. Concha, L. Ravera, and E. Rodr´ ıguez, “Three-dimensional Maxwellian extended Bargmann supergravity,”JHEP04(2020) 051,1912.09477

    work page arXiv 2020

  52. [52]

    Three-dimensional non-relativistic extended supergravity with cosmological constant,

    P. Concha, L. Ravera, and E. Rodr´ ıguez, “Three-dimensional non-relativistic extended supergravity with cosmological constant,”Eur. Phys. J. C80(2020), no. 12, 1105, 2008.08655

    work page arXiv 2020

  53. [53]

    Three-dimensional exotic Newtonian supergravity theory with cosmological constant,

    P. Concha, L. Ravera, and E. Rodr´ ıguez, “Three-dimensional exotic Newtonian supergravity theory with cosmological constant,”Eur. Phys. J. C81(2021), no. 7, 646,2104.12908

    work page arXiv 2021

  54. [54]

    Three-dimensional non-relativistic Hietarinta supergravity,

    P. Concha, E. Rodr´ ıguez, and S. Salgado, “Three-dimensional non-relativistic Hietarinta supergravity,”Eur. Phys. J. C85(2025), no. 1, 47,2409.01298

    work page arXiv 2025

  55. [55]

    Non-relativistic three-dimensional supergravity theories and semigroup expansion method,

    P. Concha, M. Ipinza, L. Ravera, and E. Rodr´ ıguez, “Non-relativistic three-dimensional supergravity theories and semigroup expansion method,”JHEP02(2021) 094,2010.01216

    work page arXiv 2021

  56. [56]

    Three-dimensional teleparallel Chern-Simons supergravity theory,

    R. Caroca, P. Concha, D. Pe˜ nafiel, and E. Rodr´ ıguez, “Three-dimensional teleparallel Chern-Simons supergravity theory,”Eur. Phys. J. C81(2021), no. 8, 762,2103.06717

    work page arXiv 2021

  57. [57]

    (2+1)-Dimensional Gravity as an Exactly Soluble System,

    E. Witten, “(2+1)-Dimensional Gravity as an Exactly Soluble System,”Nucl. Phys. B311 (1988) 46

    1988

  58. [58]

    Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008),

    J. Zanelli, “Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008),” in7th Mexican Workshop on Particles and Fields. 2, 2005.hep-th/0502193

    work page arXiv 2008

  59. [59]

    Torsional Carroll Gravity,

    P. Concha, N. Merino, L. Ravera, and E. Rodr´ ıguez, “Torsional Carroll Gravity,”Phys. Rev. Lett.136(2026), no. 10, 101402,2512.14688

    work page arXiv 2026

  60. [60]

    Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,

    J. Matulich, S. Prohazka, and J. Salzer, “Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension,”JHEP07(2019) 118,1903.09165

    work page arXiv 2019

  61. [61]

    Extended kinematical 3D gravity theories,

    P. Concha, D. Pino, L. Ravera, and E. Rodr´ ıguez, “Extended kinematical 3D gravity theories,” JHEP01(2024) 040,2310.01335

    work page arXiv 2024

  62. [62]

    Asymptotic symmetries and dynamics of three-dimensional flat supergravity,

    G. Barnich, L. Donnay, J. Matulich, and R. Troncoso, “Asymptotic symmetries and dynamics of three-dimensional flat supergravity,”JHEP08(2014) 071,1407.4275. 20

    work page arXiv 2014

  63. [63]

    Super-BMS 3 invariant boundary theory from three-dimensional flat supergravity,

    G. Barnich, L. Donnay, J. Matulich, and R. Troncoso, “Super-BMS 3 invariant boundary theory from three-dimensional flat supergravity,”JHEP01(2017) 029,1510.08824

    work page arXiv 2017

  64. [64]

    Three-dimensional Poincar´ e supergravity andN-extended supersymmetricBM S 3 algebra,

    R. Caroca, P. Concha, O. Fierro, and E. Rodr´ ıguez, “Three-dimensional Poincar´ e supergravity andN-extended supersymmetricBM S 3 algebra,”Phys. Lett. B792(2019) 93–100, 1812.05065

    work page arXiv 2019

  65. [65]

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

    P. S. Howe, J. Izquierdo, G. Papadopoulos, and P. Townsend, “New supergravities with central charges and Killing spinors in (2+1)-dimensions,”Nucl. Phys. B467(1996) 183–214, hep-th/9505032. 21

    work page arXiv 1996