Abstract
In the present work we find novel Newtonian gravity models in three space-time dimensions. We first present a Maxwellian version of the extended Newtonian gravity, which is obtained as the non-relativistic limit of a particular U(1)-enlargement of an enhanced Maxwell Chern-Simons gravity. We show that the extended Newtonian gravity appears as a particular sub-case. Then, the introduction of a cosmological constant to the Maxwellian extended Newtonian theory is also explored. To this purpose, we consider the non-relativistic limit of an enlarged symmetry. An alternative method to obtain our results is presented by applying the semigroup expansion method to the enhanced Nappi-Witten algebra. The advantages of considering the Lie algebra expansion procedure is also discussed.
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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].
M. Taylor, Lifshitz holography, Class. Quant. Grav. 33 (2016) 033001 [arXiv:1512.03554] [INSPIRE].
D.T. Son, Newton-Cartan geometry and the quantum Hall effect, arXiv:1306.0638 [INSPIRE].
C. Hoyos and D.T. Son, Hall viscosity and electromagnetic response, Phys. Rev. Lett. 108 (2012) 066805 [arXiv:1109.2651] [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].
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].
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].
J.M. Lévy-Leblond, Galilei group and Galilean invariance, in Group theory and its applications, volume II, Academic Press, New York, NY, U.S.A. (1971), pg. 221.
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].
E.A. Bergshoeff and J. Rosseel, Three-dimensional extended Bargmann supergravity, Phys. Rev. Lett. 116 (2016) 251601 [arXiv:1604.08042] [INSPIRE].
D. Hansen, J. Hartong and N.A. Obers, Action principle for Newtonian gravity, Phys. Rev. Lett. 122 (2019) 061106 [arXiv:1807.04765] [INSPIRE].
N. Ozdemir, M. Ozkan, O. Tunca and U. Zorba, Three-dimensional extended Newtonian (super)gravity, JHEP 05 (2019) 130 [arXiv:1903.09377] [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].
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].
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].
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].
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].
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.K. Concha, D.M. Penafiel, E.K. Rodriguez and P. Salgado, Chern-Simons and Born-Infeld gravity theories and Maxwell algebras type, Eur. Phys. J. C 74 (2014) 2741 [arXiv:1402.0023] [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 and E.K. Rodríguez, N = 1 supergravity and Maxwell superalgebras, JHEP 09 (2014) 090 [arXiv:1407.4635] [INSPIRE].
P.K. Concha, O. Fierro, E.K. Rodríguez and P. Salgado, Chern-Simons supergravity in D = 3 and Maxwell superalgebra, Phys. Lett. B 750 (2015) 117 [arXiv:1507.02335] [INSPIRE].
D.M. Peñafiel and L. Ravera, On the hidden Maxwell superalgebra underlying D = 4 supergravity, Fortsch. Phys. 65 (2017) 1700005 [arXiv:1701.04234] [INSPIRE].
L. Ravera, Hidden role of Maxwell superalgebras in the free differential algebras of D = 4 and D = 11 supergravity, Eur. Phys. J. C 78 (2018) 211 [arXiv:1801.08860] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, On the supersymmetry invariance of flat supergravity with boundary, JHEP 01 (2019) 192 [arXiv:1809.07871] [INSPIRE].
S. Bansal and D. Sorokin, Can Chern-Simons or Rarita-Schwinger be a Volkov-Akulov Goldstone?, JHEP 07 (2018) 106 [arXiv:1806.05945] [INSPIRE].
D. Chernyavsky, N.S. Deger and D. Sorokin, Spontaneously broken 3d Hietarinta/Maxwell Chern-Simons theory and minimal massive gravity, Eur. Phys. J. C 80 (2020) 556 [arXiv:2002.07592] [INSPIRE].
H. Bacry and J. Levy-Leblond, Possible kinematics, J. Math. Phys. 9 (1968) 1605 [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].
E. Inönü and E.P. Wigner, On the contraction of groups and their representations, Proc. Nat. Acad. Sci. U.S.A. 39 (1953) 510.
E. Weimar-Woods, Contractions, generalized Inönü-Wigner contractions and deformations of finite-dimensional Lie algebras, Rev. Math. Phys. 12 (2000) 1505.
D.V. Soroka and V.A. Soroka, Tensor extension of the Poincaré algebra, Phys. Lett. B 607 (2005) 302 [hep-th/0410012] [INSPIRE].
D.V. Soroka and V.A. Soroka, Semi-simple extension of the (super)Poincaré algebra, Adv. High Energy Phys. 2009 (2009) 234147 [hep-th/0605251] [INSPIRE].
R.-G. Cai and N. Ohta, Black holes in pure Lovelock gravities, Phys. Rev. D 74 (2006) 064001 [hep-th/0604088] [INSPIRE].
N. Dadhich, J.M. Pons and K. Prabhu, On the static Lovelock black holes, Gen. Rel. Grav. 45 (2013) 1131 [arXiv:1201.4994] [INSPIRE].
P.K. Concha, R. Durka, C. Inostroza, N. Merino and E.K. Rodríguez, Pure Lovelock gravity and Chern-Simons theory, Phys. Rev. D 94 (2016) 024055 [arXiv:1603.09424] [INSPIRE].
P.K. Concha, N. Merino and E.K. Rodŕıguez, Lovelock gravities from Born-Infeld gravity theory, Phys. Lett. B 765 (2017) 395 [arXiv:1606.07083] [INSPIRE].
P. Concha and E. Rodríguez, Generalized pure Lovelock gravity, Phys. Lett. B 774 (2017) 616 [arXiv:1708.08827] [INSPIRE].
P.K. Concha, E.K. Rodríguez and P. Salgado, Generalized supersymmetric cosmological term in N = 1 supergravity, JHEP 08 (2015) 009 [arXiv:1504.01898] [INSPIRE].
M.C. Ipinza, P.K. Concha, L. Ravera and E.K. Rodríguez, On the supersymmetric extension of Gauss-Bonnet like gravity, JHEP 09 (2016) 007 [arXiv:1607.00373] [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].
D.M. Peñafiel and L. Ravera, Generalized cosmological term in D = 4 supergravity from a new AdS-Lorentz superalgebra, Eur. Phys. J. C 78 (2018) 945 [arXiv:1807.07673] [INSPIRE].
P. Concha, R. Durka and E. Rodríguez, Resonant superalgebras and N = 1 supergravity theories in three spacetime dimensions, Phys. Lett. B 808 (2020) 135659 [arXiv:2005.11803] [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].
P. Salgado, R.J. Szabo and O. Valdivia, Topological gravity and transgression holography, Phys. Rev. D 89 (2014) 084077 [arXiv:1401.3653] [INSPIRE].
S. Hoseinzadeh and A. Rezaei-Aghdam, (2 + 1)-dimensional gravity from Maxwell and semisimple extension of the Poincaré gauge symmetric models, Phys. Rev. D 90 (2014) 084008 [arXiv:1402.0320] [INSPIRE].
P. Concha, N. Merino, O. Mišković, E. Rodríguez, P. Salgado-ReboLledó and O. Valdivia, Asymptotic symmetries of three-dimensional Chern-Simons gravity for the Maxwell algebra, JHEP 10 (2018) 079 [arXiv:1805.08834] [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].
P. Concha, N -extended Maxwell supergravities as Chern-Simons theories in three spacetime dimensions, Phys. Lett. B 792 (2019) 290 [arXiv:1903.03081] [INSPIRE].
J. Diaz et al., A generalized action for (2 + 1)-dimensional Chern-Simons gravity, J. Phys. A 45 (2012) 255207 [arXiv:1311.2215] [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. Concha, N. Merino, E. Rodríguez, P. Salgado-ReboLledó and O. Valdivia, Semi-simple enlargement of the \( {\mathfrak{bms}}_3 \) algebra from a \( \mathfrak{so} \)(2, 2) ⊕ \( \mathfrak{so} \)(2, 1) Chern-Simons theory, JHEP 02 (2019) 002 [arXiv:1810.12256] [INSPIRE].
E. Witten, (2+1)-Dimensional Gravity as an Exactly Soluble System, Nucl. Phys. B 311 (1988) 46 [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].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional Maxwellian extended Bargmann supergravity, JHEP 04 (2020) 051 [arXiv:1912.09477] [INSPIRE].
A. Barducci, R. Casalbuoni and J. Gomis, Nonrelativistic k-contractions of the coadjoint Poincaré algebra, Int. J. Mod. Phys. A 35 (2020) 2050009 [arXiv:1910.11682] [INSPIRE].
A. Barducci, R. Casalbuoni and J. Gomis, A particle model with extra dimensions from Coadjoint Poincaré Symmetry, JHEP 08 (2020) 092 [arXiv:2006.11725] [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, 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].
J.A. de Azcarraga, J.M. Izquierdo, M. Picón and O. Varela, Extensions, expansions, Lie algebra cohomology and enlarged superspaces, Class. Quant. Grav. 21 (2004) S1375 [hep-th/0401033] [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].
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].
L. Romano, Non-Relativistic Four Dimensional p-Brane Supersymmetric Theories and Lie Algebra Expansion, arXiv:1906.08220 [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].
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].
A. Fontanella and L. Romano, Lie Algebra Expansion and Integrability in Superstring σ-models, JHEP 20 (2020) 083 [arXiv:2005.01736] [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].
R. Caroca, P. Concha, E. Rodríguez and P. Salgado-ReboLledó, Generalizing the \( {\mathfrak{bms}}_3 \) 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 BM S3 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].
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].
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 Schr¨odinger supergravity, JHEP 11 (2015) 180 [arXiv:1509.04527] [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].
G. Festuccia and N. Seiberg, Rigid Supersymmetric Theories in Curved Superspace, JHEP 06 (2011) 114 [arXiv:1105.0689] [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].
M. Mariño, Lectures on non-perturbative effects in large N gauge theories, matrix models and strings, Fortsch. Phys. 62 (2014) 455 [arXiv:1206.6272] [INSPIRE].
E. Bergshoeff, D. Grumiller, S. Prohazka and J. Rosseel, Three-dimensional Spin-3 Theories Based on General Kinematical Algebras, JHEP 01 (2017) 114 [arXiv:1612.02277] [INSPIRE].
E. Bergshoeff, J. Gomis, B. Rollier, J. Rosseel and T. ter Veldhuis, Carroll versus Galilei Gravity, JHEP 03 (2017) 165 [arXiv:1701.06156] [INSPIRE].
J. Matulich, S. Prohazka and J. Salzer, Limits of three-dimensional gravity and metric kinematical Lie algebras in any dimension, JHEP 07 (2019) 118 [arXiv:1903.09165] [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, N-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions, JHEP 02 (2020) 128 [arXiv:1912.04172] [INSPIRE].
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Concha, P., Ravera, L., Rodríguez, E. et al. Three-dimensional Maxwellian extended Newtonian gravity and flat limit. J. High Energ. Phys. 2020, 181 (2020). https://doi.org/10.1007/JHEP10(2020)181
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DOI: https://doi.org/10.1007/JHEP10(2020)181