Abstract
In this work we present an alternative method to construct diverse non-relativistic Chern-Simons supergravity theories in three spacetime dimensions. To this end, we apply the Lie algebra expansion method based on semigroups to a supersymmetric extension of the Nappi-Witten algebra. Two different families of non-relativistic superalgebras are obtained, corresponding to generalizations of the extended Bargmann superalgebra and extended Newton-Hooke superalgebra, respectively. The expansion method considered here allows to obtain known and new non-relativistic supergravity models in a systematic way. In particular, it immediately provides an invariant tensor for the expanded superalgebra, which is essential to construct the corresponding Chern-Simons supergravity action. We show that the extended Bargmann supergravity and its Maxwellian generalization appear as particular subcases of a generalized extended Bargmann supergravity theory. In addition, we demonstrate that the generalized extended Bargmann and generalized extended Newton-Hooke supergravity families are related through a contraction process.
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R. Andringa, E.A. Bergshoeff, J. Rosseel and E. Sezgin, 3D Newton-Cartan supergravity, Class. Quant. Grav. 30 (2013) 205005 [arXiv:1305.6737] [INSPIRE].
E. Bergshoeff, J. Rosseel and T. Zojer, Newton-Cartan supergravity with torsion and Schrödinger supergravity, JHEP 11 (2015) 180 [arXiv:1509.04527] [INSPIRE].
E.A. Bergshoeff and J. Rosseel, Three-dimensional extended Bargmann supergravity, Phys. Rev. Lett. 116 (2016) 251601 [arXiv:1604.08042] [INSPIRE].
N. Ozdemir, M. Ozkan, O. Tunca and U. Zorba, Three-dimensional extended Newtonian (super)gravity, JHEP 05 (2019) 130 [arXiv:1903.09377] [INSPIRE].
J.A. de Azcárraga, D. Gútiez and J.M. Izquierdo, Extended D = 3 Bargmann supergravity from a Lie algebra expansion, Nucl. Phys. B 946 (2019) 114706 [arXiv:1904.12786] [INSPIRE].
N. Ozdemir, M. Ozkan and U. Zorba, Three-dimensional extended Lifshitz, Schrödinger and Newton-Hooke supergravity, JHEP 11 (2019) 052 [arXiv:1909.10745] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional Maxwellian extended Bargmann supergravity, JHEP 04 (2020) 051 [arXiv:1912.09477] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional non-relativistic extended supergravity with cosmological constant, Eur. Phys. J. C 80 (2020) 1105 [arXiv:2008.08655] [INSPIRE].
R. Grassie, Generalised Bargmann superalgebras, arXiv:2010.01894 [INSPIRE].
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie), Ann. Ecole Norm. Sup. 40 (1923) 325.
E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie) (suite), Ann. Ecole Norm. Sup. 41 (1924) 1.
C. Duval and H.P. Kunzle, Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation, Gen. Rel. Grav. 16 (1984) 333 [INSPIRE].
C. Duval, G. Burdet, H.P. Kunzle and M. Perrin, Bargmann structures and Newton-Cartan theory, Phys. Rev. D 31 (1985) 1841 [INSPIRE].
C. Duval and P.A. Horvathy, Non-relativistic conformal symmetries and Newton-Cartan structures, J. Phys. A 42 (2009) 465206 [arXiv:0904.0531] [INSPIRE].
R. Andringa, E. Bergshoeff, S. Panda and M. de Roo, Newtonian gravity and the Bargmann algebra, Class. Quant. Grav. 28 (2011) 105011 [arXiv:1011.1145] [INSPIRE].
R. Banerjee, A. Mitra and P. Mukherjee, Localization of the Galilean symmetry and dynamical realization of Newton-Cartan geometry, Class. Quant. Grav. 32 (2015) 045010 [arXiv:1407.3617] [INSPIRE].
R. Banerjee and P. Mukherjee, Torsional Newton-Cartan geometry from Galilean gauge theory, Class. Quant. Grav. 33 (2016) 225013 [arXiv:1604.06893] [INSPIRE].
E. Bergshoeff, A. Chatzistavrakidis, L. Romano and J. Rosseel, Newton-Cartan gravity and torsion, JHEP 10 (2017) 194 [arXiv:1708.05414] [INSPIRE].
L. Avilés, E. Frodden, J. Gomis, D. Hidalgo and J. Zanelli, Non-relativistic Maxwell Chern-Simons gravity, JHEP 05 (2018) 047 [arXiv:1802.08453] [INSPIRE].
L. Avilés, J. Gomis and D. Hidalgo, Stringy (Galilei) Newton-Hooke Chern-Simons Gravities, JHEP 09 (2019) 015 [arXiv:1905.13091] [INSPIRE].
D. Chernyavsky and D. Sorokin, Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries, JHEP 07 (2019) 156 [arXiv:1905.13154] [INSPIRE].
P. Concha and E. Rodríguez, Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra, JHEP 07 (2019) 085 [arXiv:1906.00086] [INSPIRE].
T. Harmark, J. Hartong, L. Menculini, N.A. Obers and G. Oling, Relating non-relativistic string theories, JHEP 11 (2019) 071 [arXiv:1907.01663] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Non-relativistic gravity and its coupling to matter, JHEP 06 (2020) 145 [arXiv:2001.10277] [INSPIRE].
M. Ergen, E. Hamamci and D. Van den Bleeken, Oddity in nonrelativistic, strong gravity, Eur. Phys. J. C 80 (2020) 563 [Erratum ibid. 80 (2020) 657] [arXiv:2002.02688] [INSPIRE].
O. Kasikci, N. Ozdemir, M. Ozkan and U. Zorba, Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions, JHEP 04 (2020) 067 [arXiv:2002.03558] [INSPIRE].
P. Concha, M. Ipinza and E. Rodríguez, Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions, Phys. Lett. B 807 (2020) 135593 [arXiv:2004.01203] [INSPIRE].
D.T. Son, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D 78 (2008) 046003 [arXiv:0804.3972] [INSPIRE].
K. Balasubramanian and J. McGreevy, Gravity duals for non-relativistic CFTs, Phys. Rev. Lett. 101 (2008) 061601 [arXiv:0804.4053] [INSPIRE].
S. Kachru, X. Liu and M. Mulligan, Gravity duals of Lifshitz-like fixed points, Phys. Rev. D 78 (2008) 106005 [arXiv:0808.1725] [INSPIRE].
A. Bagchi and R. Gopakumar, Galilean conformal algebras and AdS/CFT, JHEP 07 (2009) 037 [arXiv:0902.1385] [INSPIRE].
A. Bagchi, R. Gopakumar, I. Mandal and A. Miwa, GCA in 2d, JHEP 08 (2010) 004 [arXiv:0912.1090] [INSPIRE].
M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Torsional Newton-Cartan geometry and Lifshitz holography, Phys. Rev. D 89 (2014) 061901 [arXiv:1311.4794] [INSPIRE].
M.H. Christensen, J. Hartong, N.A. Obers and B. Rollier, Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography, JHEP 01 (2014) 057 [arXiv:1311.6471] [INSPIRE].
J. Hartong, E. Kiritsis and N.A. Obers, Lifshitz space-times for Schrödinger holography, Phys. Lett. B 746 (2015) 318 [arXiv:1409.1519] [INSPIRE].
J. Hartong, E. Kiritsis and N.A. Obers, Schrödinger invariance from Lifshitz isometries in holography and field theory, Phys. Rev. D 92 (2015) 066003 [arXiv:1409.1522] [INSPIRE].
J. Hartong, E. Kiritsis and N.A. Obers, Field theory on Newton-Cartan backgrounds and symmetries of the Lifshitz vacuum, JHEP 08 (2015) 006 [arXiv:1502.00228] [INSPIRE].
M. Taylor, Lifshitz holography, Class. Quant. Grav. 33 (2016) 033001 [arXiv:1512.03554] [INSPIRE].
C. Hoyos and D.T. Son, Hall viscosity and electromagnetic response, Phys. Rev. Lett. 108 (2012) 066805 [arXiv:1109.2651] [INSPIRE].
D.T. Son, Newton-Cartan geometry and the quantum Hall effect, arXiv:1306.0638 [INSPIRE].
A.G. Abanov and A. Gromov, Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field, Phys. Rev. B 90 (2014) 014435 [arXiv:1401.3703] [INSPIRE].
M. Geracie, K. Prabhu and M.M. Roberts, Curved non-relativistic spacetimes, Newtonian gravitation and massive matter, J. Math. Phys. 56 (2015) 103505 [arXiv:1503.02682] [INSPIRE].
A. Gromov, K. Jensen and A.G. Abanov, Boundary effective action for quantum Hall states, Phys. Rev. Lett. 116 (2016) 126802 [arXiv:1506.07171] [INSPIRE].
D.R. Grigore, The projective unitary irreducible representations of the Galilei group in (1 + 2)-dimensions, J. Math. Phys. 37 (1996) 460 [hep-th/9312048] [INSPIRE].
S.K. Bose, The Galilean group in (2 + 1) space-times and its central extension, Commun. Math. Phys. 169 (1995) 385 [INSPIRE].
C. Duval and P.A. Horvathy, The ‘Peierls substitution’ and the exotic Galilei group, Phys. Lett. B 479 (2000) 284 [hep-th/0002233] [INSPIRE].
R. Jackiw and V.P. Nair, Anyon spin and the exotic central extension of the planar Galilei group, Phys. Lett. B 480 (2000) 237 [hep-th/0003130] [INSPIRE].
G. Papageorgiou and B.J. Schroers, A Chern-Simons approach to Galilean quantum gravity in 2 + 1 dimensions, JHEP 11 (2009) 009 [arXiv:0907.2880] [INSPIRE].
A. Achucarro and P.K. Townsend, A Chern-Simons action for three-dimensional Anti-de Sitter supergravity theories, Phys. Lett. B 180 (1986) 89 [INSPIRE].
E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B 311 (1988) 46 [INSPIRE].
J. Zanelli, Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008), hep-th/0502193 [INSPIRE].
J.A. de Azcarraga, J.M. Izquierdo, M. Picón and O. Varela, Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity, Nucl. Phys. B 662 (2003) 185 [hep-th/0212347] [INSPIRE].
F. Izaurieta, E. Rodriguez and P. Salgado, Expanding Lie (super)algebras through Abelian semigroups, J. Math. Phys. 47 (2006) 123512 [hep-th/0606215] [INSPIRE].
M. Hatsuda and M. Sakaguchi, Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction, Prog. Theor. Phys. 109 (2003) 853 [hep-th/0106114] [INSPIRE].
J.A. de Azcarraga, J.M. Izquierdo, M. Picón and O. Varela, Expansions of algebras and superalgebras and some applications, Int. J. Theor. Phys. 46 (2007) 2738 [hep-th/0703017] [INSPIRE].
R. Caroca, I. Kondrashuk, N. Merino and F. Nadal, Bianchi spaces and their three-dimensional isometries as S-expansions of two-dimensional isometries, J. Phys. A 46 (2013) 225201 [arXiv:1104.3541] [INSPIRE].
L. Andrianopoli, N. Merino, F. Nadal and M. Trigiante, General properties of the expansion methods of Lie algebras, J. Phys. A 46 (2013) 365204 [arXiv:1308.4832] [INSPIRE].
M. Artebani, R. Caroca, M.C. Ipinza, D.M. Peñafiel and P. Salgado, Geometrical aspects of the Lie algebra S-expansion procedure, J. Math. Phys. 57 (2016) 023516 [arXiv:1602.04525] [INSPIRE].
M.C. Ipinza, F. Lingua, D.M. Peñafiel and L. Ravera, An analytic method for S-expansion involving resonance and reduction, Fortsch. Phys. 64 (2016) 854 [arXiv:1609.05042] [INSPIRE].
C. Inostroza, I. Kondrashuk, N. Merino and F. Nadal, A Java library to perform S-expansions of Lie algebras, arXiv:1703.04036 [INSPIRE].
C. Inostroza, I. Kondrashuk, N. Merino and F. Nadal, On the algorithm to find S-related Lie algebras, J. Phys. Conf. Ser. 1085 (2018) 052011 [arXiv:1802.05765] [INSPIRE].
E. Bergshoeff, J.M. Izquierdo, T. Ortín and L. Romano, Lie algebra expansions and actions for non-relativistic gravity, JHEP 08 (2019) 048 [arXiv:1904.08304] [INSPIRE].
L. Romano, Non-relativistic four dimensional p-brane supersymmetric theories and Lie algebra expansion, arXiv:1906.08220 [INSPIRE].
A. Fontanella and L. Romano, Lie algebra expansion and integrability in superstring σ-models, JHEP 07 (2020) 083 [arXiv:2005.01736] [INSPIRE].
D.M. Peñafiel and P. Salgado-ReboLledó, Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra, Phys. Lett. B 798 (2019) 135005 [arXiv:1906.02161] [INSPIRE].
J. Gomis, A. Kleinschmidt, J. Palmkvist and P. Salgado-ReboLledó, Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity, JHEP 02 (2020) 009 [arXiv:1912.07564] [INSPIRE].
E. Bergshoeff, J. Gomis and P. Salgado-ReboLledó, Non-relativistic limits and three-dimensional coadjoint Poincaré gravity, Proc. Roy. Soc. Lond. A 476 (2020) 20200106 [arXiv:2001.11790] [INSPIRE].
P. Concha, L. Ravera, E. Rodríguez and G. Rubio, Three-dimensional Maxwellian extended Newtonian gravity and flat limit, JHEP 10 (2020) 181 [arXiv:2006.13128] [INSPIRE].
F. Izaurieta, E. Rodriguez, P. Minning, P. Salgado and A. Perez, Standard general relativity from Chern-Simons gravity, Phys. Lett. B 678 (2009) 213 [arXiv:0905.2187] [INSPIRE].
J. Diaz, O. Fierro, F. Izaurieta, N. Merino, E. Rodriguez, P. Salgado et al., A generalized action for (2 + 1)-dimensional Chern-Simons gravity, J. Phys. A 45 (2012) 255207 [arXiv:1311.2215] [INSPIRE].
P.K. Concha, D.M. Peñafiel, E.K. Rodríguez and P. Salgado, Even-dimensional general relativity from Born-Infeld gravity, Phys. Lett. B 725 (2013) 419 [arXiv:1309.0062] [INSPIRE].
P. Salgado and S. Salgado, \( \mathfrak{so}\left(D-1,1\right)\otimes \mathfrak{so}\left(D-1,2\right) \) algebras and gravity, Phys. Lett. B 728 (2014) 5 [INSPIRE].
R. Caroca, P. Concha, O. Fierro, E. Rodríguez and P. Salgado-ReboLledó, Generalized Chern-Simons higher-spin gravity theories in three dimensions, Nucl. Phys. B 934 (2018) 240 [arXiv:1712.09975] [INSPIRE].
F. Izaurieta, E. Rodriguez and P. Salgado, Eleven-dimensional gauge theory for the M algebra as an Abelian semigroup expansion of osp(32|1), Eur. Phys. J. C 54 (2008) 675 [hep-th/0606225] [INSPIRE].
O. Fierro, F. Izaurieta, P. Salgado and O. Valdivia, Minimal AdS-Lorentz supergravity in three-dimensions, Phys. Lett. B 788 (2019) 198 [arXiv:1401.3697] [INSPIRE].
P.K. Concha and E.K. Rodríguez, N = 1 supergravity and Maxwell superalgebras, JHEP 09 (2014) 090 [arXiv:1407.4635] [INSPIRE].
P.K. Concha, O. Fierro and E.K. Rodríguez, Inönü-Wigner contraction and D = 2 + 1 supergravity, Eur. Phys. J. C 77 (2017) 48 [arXiv:1611.05018] [INSPIRE].
A. Banaudi and L. Ravera, Generalized AdS-Lorentz deformed supergravity on a manifold with boundary, Eur. Phys. J. Plus 133 (2018) 514 [arXiv:1803.08738] [INSPIRE].
P. Concha, D.M. Peñafiel and E. Rodríguez, On the Maxwell supergravity and flat limit in 2 + 1 dimensions, Phys. Lett. B 785 (2018) 247 [arXiv:1807.00194] [INSPIRE].
R. Caroca, P. Concha, E. Rodríguez and P. Salgado-ReboLledó, Generalizing the bms3 and 2D-conformal algebras by expanding the Virasoro algebra, Eur. Phys. J. C 78 (2018) 262 [arXiv:1707.07209] [INSPIRE].
R. Caroca, P. Concha, O. Fierro and E. Rodríguez, Three-dimensional Poincaré supergravity and N -extended supersymmetric BMS3 algebra, Phys. Lett. B 792 (2019) 93 [arXiv:1812.05065] [INSPIRE].
R. Caroca, P. Concha, O. Fierro and E. Rodríguez, On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions, Eur. Phys. J. C 80 (2020) 29 [arXiv:1908.09150] [INSPIRE].
C.R. Nappi and E. Witten, A WZW model based on a nonsemisimple group, Phys. Rev. Lett. 71 (1993) 3751 [hep-th/9310112] [INSPIRE].
J.M. Figueroa-O’Farrill and S. Stanciu, More D-branes in the Nappi-Witten background, JHEP 01 (2000) 024 [hep-th/9909164] [INSPIRE].
E. Inonu and E.P. Wigner, On the contraction of groups and their represenations, Proc. Nat. Acad. Sci. 39 (1953) 510 [INSPIRE].
J.D. Edelstein, M. Hassaine, R. Troncoso and J. Zanelli, Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian, Phys. Lett. B 640 (2006) 278 [hep-th/0605174] [INSPIRE].
R. Schrader, The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys. 20 (1972) 701 [INSPIRE].
H. Bacry, P. Combe and J.L. Richard, Group-theoretical analysis of elementary particles in an external electromagnetic field. 1. The relativistic particle in a constant and uniform field, Nuovo Cim. A 67 (1970) 267 [INSPIRE].
J. Gomis and A. Kleinschmidt, On free Lie algebras and particles in electro-magnetic fields, JHEP 07 (2017) 085 [arXiv:1705.05854] [INSPIRE].
P.K. Concha and E.K. Rodríguez, Maxwell superalgebras and Abelian semigroup expansion, Nucl. Phys. B 886 (2014) 1128 [arXiv:1405.1334] [INSPIRE].
R. Aldrovandi, A.L. Barbosa, L.C.B. Crispino and J.G. Pereira, Non-relativistic spacetimes with cosmological constant, Class. Quant. Grav. 16 (1999) 495 [gr-qc/9801100] [INSPIRE].
G.W. Gibbons and C.E. Patricot, Newton-Hooke space-times, Hpp waves and the cosmological constant, Class. Quant. Grav. 20 (2003) 5225 [hep-th/0308200] [INSPIRE].
J. Brugues, J. Gomis and K. Kamimura, Newton-Hooke algebras, non-relativistic branes and generalized pp-wave metrics, Phys. Rev. D 73 (2006) 085011 [hep-th/0603023] [INSPIRE].
P.D. Alvarez, J. Gomis, K. Kamimura and M.S. Plyushchay, (2 + 1)D exotic Newton-Hooke symmetry, duality and projective phase, Annals Phys. 322 (2007) 1556 [hep-th/0702014] [INSPIRE].
G. Papageorgiou and B.J. Schroers, Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra, JHEP 11 (2010) 020 [arXiv:1008.0279] [INSPIRE].
C. Duval and P. Horvathy, Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes, J. Phys. A 44 (2011) 335203 [arXiv:1104.1502] [INSPIRE].
J. Hartong, Y. Lei and N.A. Obers, Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity, Phys. Rev. D 94 (2016) 065027 [arXiv:1604.08054] [INSPIRE].
C. Duval, G. Gibbons and P. Horvathy, Conformal and projective symmetries in Newtonian cosmology, J. Geom. Phys. 112 (2017) 197 [arXiv:1605.00231] [INSPIRE].
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 (1996) 183 [hep-th/9505032] [INSPIRE].
A. Giacomini, R. Troncoso and S. Willison, Three-dimensional supergravity reloaded, Class. Quant. Grav. 24 (2007) 2845 [hep-th/0610077] [INSPIRE].
R. Troncoso and J. Zanelli, Higher dimensional gravity, propagating torsion and AdS gauge invariance, Class. Quant. Grav. 17 (2000) 4451 [hep-th/9907109] [INSPIRE].
P.K. Concha, D.M. Peñafiel, E.K. Rodríguez and P. Salgado, Generalized Poincaré algebras and Lovelock-Cartan gravity theory, Phys. Lett. B 742 (2015) 310 [arXiv:1405.7078] [INSPIRE].
P.K. Concha, R. Durka, N. Merino and E.K. Rodríguez, New family of Maxwell like algebras, Phys. Lett. B 759 (2016) 507 [arXiv:1601.06443] [INSPIRE].
H.R. Afshar, E.A. Bergshoeff, A. Mehra, P. Parekh and B. Rollier, A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities, JHEP 04 (2016) 145 [arXiv:1512.06277] [INSPIRE].
V. Pestun, Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys. 313 (2012) 71 [arXiv:0712.2824] [INSPIRE].
G. Festuccia and N. Seiberg, Rigid supersymmetric theories in curved superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional exotic Newtonian gravity with cosmological constant, Phys. Lett. B 804 (2020) 135392 [arXiv:1912.02836] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Action principle for Newtonian gravity, Phys. Rev. Lett. 122 (2019) 061106 [arXiv:1807.04765] [INSPIRE].
L. Ravera, AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit, Phys. Lett. B 795 (2019) 331 [arXiv:1905.00766] [INSPIRE].
F. Ali and L. Ravera, \( \mathcal{N} \)-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions, JHEP 02 (2020) 128 [arXiv:1912.04172] [INSPIRE].
L. Ciambelli, C. Marteau, A.C. Petkou, P.M. Petropoulos and K. Siampos, Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Class. Quant. Grav. 35 (2018) 165001 [arXiv:1802.05286] [INSPIRE].
L. Ciambelli, C. Marteau, A.C. Petkou, P.M. Petropoulos and K. Siampos, Flat holography and Carrollian fluids, JHEP 07 (2018) 165 [arXiv:1802.06809] [INSPIRE].
L. Ciambelli and C. Marteau, Carrollian conservation laws and Ricci-flat gravity, Class. Quant. Grav. 36 (2019) 085004 [arXiv:1810.11037] [INSPIRE].
A. Campoleoni, L. Ciambelli, C. Marteau, P.M. Petropoulos and K. Siampos, Two-dimensional fluids and their holographic duals, Nucl. Phys. B 946 (2019) 114692 [arXiv:1812.04019] [INSPIRE].
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Concha, P., Ipinza, M., Ravera, L. et al. Non-relativistic three-dimensional supergravity theories and semigroup expansion method. J. High Energ. Phys. 2021, 94 (2021). https://doi.org/10.1007/JHEP02(2021)094
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DOI: https://doi.org/10.1007/JHEP02(2021)094