×

Non-relativistic three-dimensional supergravity theories and semigroup expansion method. (English) Zbl 1460.83111

Summary: 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.

MSC:

83E50 Supergravity
58J28 Eta-invariants, Chern-Simons invariants
81R10 Infinite-dimensional groups and algebras motivated by physics, including Virasoro, Kac-Moody, \(W\)-algebras and other current algebras and their representations

Software:

S-expansion
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Andringa, R.; Bergshoeff, EA; Rosseel, J.; Sezgin, E., 3D Newton-Cartan supergravity, Class. Quant. Grav., 30, 205005 (2013) · Zbl 1276.83035
[2] Bergshoeff, E.; Rosseel, J.; Zojer, T., Newton-Cartan supergravity with torsion and Schrödinger supergravity, JHEP, 11, 180 (2015) · Zbl 1388.83743
[3] Bergshoeff, EA; Rosseel, J., Three-dimensional extended Bargmann supergravity, Phys. Rev. Lett., 116, 251601 (2016)
[4] Ozdemir, N.; Ozkan, M.; Tunca, O.; Zorba, U., Three-dimensional extended Newtonian (super)gravity, JHEP, 05, 130 (2019) · Zbl 1416.83078
[5] de Azcárraga, JA; Gútiez, D.; Izquierdo, JM, Extended D = 3 Bargmann supergravity from a Lie algebra expansion, Nucl. Phys. B, 946, 114706 (2019) · Zbl 1430.83099
[6] Ozdemir, N.; Ozkan, M.; Zorba, U., Three-dimensional extended Lifshitz, Schrödinger and Newton-Hooke supergravity, JHEP, 11, 052 (2019) · Zbl 1429.83103
[7] Concha, P.; Ravera, L.; Rodríguez, E., Three-dimensional Maxwellian extended Bargmann supergravity, JHEP, 04, 051 (2020) · Zbl 1436.83094
[8] Concha, P.; Ravera, L.; Rodríguez, E., Three-dimensional non-relativistic extended supergravity with cosmological constant, Eur. Phys. J. C, 80, 1105 (2020)
[9] R. Grassie, Generalised Bargmann superalgebras, arXiv:2010.01894 [INSPIRE].
[10] E. Cartan, Sur les variétés à connexion affine et la théorie de la relativité généralisée (première partie), Ann. Ecole Norm. Sup.40 (1923) 325. · JFM 49.0542.02
[11] 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. · JFM 51.0581.01
[12] Duval, C.; Kunzle, HP, Minimal gravitational coupling in the Newtonian theory and the covariant Schrödinger equation, Gen. Rel. Grav., 16, 333 (1984)
[13] Duval, C.; Burdet, G.; Kunzle, HP; Perrin, M., Bargmann structures and Newton-Cartan theory, Phys. Rev. D, 31, 1841 (1985)
[14] Duval, C.; Horvathy, PA, Non-relativistic conformal symmetries and Newton-Cartan structures, J. Phys. A, 42, 465206 (2009) · Zbl 1180.37078
[15] Andringa, R.; Bergshoeff, E.; Panda, S.; de Roo, M., Newtonian gravity and the Bargmann algebra, Class. Quant. Grav., 28, 105011 (2011) · Zbl 1217.83019
[16] Banerjee, R.; Mitra, A.; Mukherjee, P., Localization of the Galilean symmetry and dynamical realization of Newton-Cartan geometry, Class. Quant. Grav., 32 (2015) · Zbl 1308.83126
[17] Banerjee, R.; Mukherjee, P., Torsional Newton-Cartan geometry from Galilean gauge theory, Class. Quant. Grav., 33, 225013 (2016) · Zbl 1351.83038
[18] Bergshoeff, E.; Chatzistavrakidis, A.; Romano, L.; Rosseel, J., Newton-Cartan gravity and torsion, JHEP, 10, 194 (2017) · Zbl 1383.83106
[19] Avilés, L.; Frodden, E.; Gomis, J.; Hidalgo, D.; Zanelli, J., Non-relativistic Maxwell Chern-Simons gravity, JHEP, 05, 047 (2018) · Zbl 1391.81114
[20] Avilés, L.; Gomis, J.; Hidalgo, D., Stringy (Galilei) Newton-Hooke Chern-Simons Gravities, JHEP, 09, 015 (2019) · Zbl 1423.83046
[21] Chernyavsky, D.; Sorokin, D., Three-dimensional (higher-spin) gravities with extended Schrödinger and l-conformal Galilean symmetries, JHEP, 07, 156 (2019) · Zbl 1418.83037
[22] Concha, P.; Rodríguez, E., Non-relativistic gravity theory based on an enlargement of the extended Bargmann algebra, JHEP, 07, 085 (2019) · Zbl 1418.83043
[23] Harmark, T.; Hartong, J.; Menculini, L.; Obers, NA; Oling, G., Relating non-relativistic string theories, JHEP, 11, 071 (2019) · Zbl 1429.83091
[24] Hansen, D.; Hartong, J.; Obers, NA, Non-relativistic gravity and its coupling to matter, JHEP, 06, 145 (2020) · Zbl 1437.83016
[25] M. Ergen, E. Hamamci and D. Van den Bleeken, Oddity in nonrelativistic, strong gravity, Eur. Phys. J. C80 (2020) 563 [Erratum ibid.80 (2020) 657] [arXiv:2002.02688] [INSPIRE].
[26] Kasikci, O.; Ozdemir, N.; Ozkan, M.; Zorba, U., Three-dimensional higher-order Schrödinger algebras and Lie algebra expansions, JHEP, 04, 067 (2020) · Zbl 1436.81057
[27] Concha, P.; Ipinza, M.; Rodríguez, E., Generalized Maxwellian exotic Bargmann gravity theory in three spacetime dimensions, Phys. Lett. B, 807, 135593 (2020) · Zbl 1473.83066
[28] Son, DT, Toward an AdS/cold atoms correspondence: a geometric realization of the Schrödinger symmetry, Phys. Rev. D, 78 (2008)
[29] Balasubramanian, K.; McGreevy, J., Gravity duals for non-relativistic CFTs, Phys. Rev. Lett., 101 (2008) · Zbl 1228.81247
[30] Kachru, S.; Liu, X.; Mulligan, M., Gravity duals of Lifshitz-like fixed points, Phys. Rev. D, 78, 106005 (2008)
[31] Bagchi, A.; Gopakumar, R., Galilean conformal algebras and AdS/CFT, JHEP, 07, 037 (2009)
[32] Bagchi, A.; Gopakumar, R.; Mandal, I.; Miwa, A., GCA in 2d, JHEP, 08, 004 (2010) · Zbl 1291.81346
[33] Christensen, MH; Hartong, J.; Obers, NA; Rollier, B., Torsional Newton-Cartan geometry and Lifshitz holography, Phys. Rev. D, 89 (2014) · Zbl 1333.81236
[34] Christensen, MH; Hartong, J.; Obers, NA; Rollier, B., Boundary stress-energy tensor and Newton-Cartan geometry in Lifshitz holography, JHEP, 01, 057 (2014) · Zbl 1333.81236
[35] Hartong, J.; Kiritsis, E.; Obers, NA, Lifshitz space-times for Schrödinger holography, Phys. Lett. B, 746, 318 (2015) · Zbl 1343.81224
[36] Hartong, J.; Kiritsis, E.; Obers, NA, Schrödinger invariance from Lifshitz isometries in holography and field theory, Phys. Rev. D, 92 (2015)
[37] Hartong, J.; Kiritsis, E.; Obers, NA, Field theory on Newton-Cartan backgrounds and symmetries of the Lifshitz vacuum, JHEP, 08, 006 (2015) · Zbl 1388.83258
[38] Taylor, M., Lifshitz holography, Class. Quant. Grav., 33 (2016) · Zbl 1332.83004
[39] Hoyos, C.; Son, DT, Hall viscosity and electromagnetic response, Phys. Rev. Lett., 108 (2012)
[40] D.T. Son, Newton-Cartan geometry and the quantum Hall effect, arXiv:1306.0638 [INSPIRE].
[41] Abanov, AG; Gromov, A., Electromagnetic and gravitational responses of two-dimensional noninteracting electrons in a background magnetic field, Phys. Rev. B, 90 (2014)
[42] Geracie, M.; Prabhu, K.; Roberts, MM, Curved non-relativistic spacetimes, Newtonian gravitation and massive matter, J. Math. Phys., 56, 103505 (2015) · Zbl 1327.83218
[43] Gromov, A.; Jensen, K.; Abanov, AG, Boundary effective action for quantum Hall states, Phys. Rev. Lett., 116, 126802 (2016)
[44] Grigore, DR, The projective unitary irreducible representations of the Galilei group in (1 + 2)-dimensions, J. Math. Phys., 37, 460 (1996) · Zbl 0869.22015
[45] Bose, SK, The Galilean group in (2 + 1) space-times and its central extension, Commun. Math. Phys., 169, 385 (1995) · Zbl 0826.22020
[46] Duval, C.; Horvathy, PA, The ‘Peierls substitution’ and the exotic Galilei group, Phys. Lett. B, 479, 284 (2000) · Zbl 1050.81568
[47] Jackiw, R.; Nair, VP, Anyon spin and the exotic central extension of the planar Galilei group, Phys. Lett. B, 480, 237 (2000) · Zbl 0989.81036
[48] Papageorgiou, G.; Schroers, BJ, A Chern-Simons approach to Galilean quantum gravity in 2 + 1 dimensions, JHEP, 11, 009 (2009)
[49] Achucarro, A.; Townsend, PK, A Chern-Simons action for three-dimensional Anti-de Sitter supergravity theories, Phys. Lett. B, 180, 89 (1986)
[50] E. Witten, (2 + 1)-dimensional gravity as an exactly soluble system, Nucl. Phys. B311 (1988) 46 [INSPIRE]. · Zbl 1258.83032
[51] J. Zanelli, Lecture notes on Chern-Simons (super-)gravities. Second edition (February 2008), hep-th/0502193 [INSPIRE].
[52] de Azcarraga, JA; Izquierdo, JM; Picón, M.; Varela, O., Generating Lie and gauge free differential (super)algebras by expanding Maurer-Cartan forms and Chern-Simons supergravity, Nucl. Phys. B, 662, 185 (2003) · Zbl 1022.22022
[53] Izaurieta, F.; Rodriguez, E.; Salgado, P., Expanding Lie (super)algebras through Abelian semigroups, J. Math. Phys., 47, 123512 (2006) · Zbl 1112.17005
[54] Hatsuda, M.; Sakaguchi, M., Wess-Zumino term for the AdS superstring and generalized Inonu-Wigner contraction, Prog. Theor. Phys., 109, 853 (2003) · Zbl 1059.81150
[55] de Azcarraga, JA; Izquierdo, JM; Picón, M.; Varela, O., Expansions of algebras and superalgebras and some applications, Int. J. Theor. Phys., 46, 2738 (2007) · Zbl 1128.17004
[56] Caroca, R.; Kondrashuk, I.; Merino, N.; Nadal, F., Bianchi spaces and their three-dimensional isometries as S-expansions of two-dimensional isometries, J. Phys. A, 46, 225201 (2013) · Zbl 1269.83020
[57] Andrianopoli, L.; Merino, N.; Nadal, F.; Trigiante, M., General properties of the expansion methods of Lie algebras, J. Phys. A, 46, 365204 (2013) · Zbl 1276.83034
[58] Artebani, M.; Caroca, R.; Ipinza, MC; Peñafiel, DM; Salgado, P., Geometrical aspects of the Lie algebra S-expansion procedure, J. Math. Phys., 57 (2016) · Zbl 1367.17007
[59] Ipinza, MC; Lingua, F.; Peñafiel, DM; Ravera, L., An analytic method for S-expansion involving resonance and reduction, Fortsch. Phys., 64, 854 (2016) · Zbl 1371.17020
[60] C. Inostroza, I. Kondrashuk, N. Merino and F. Nadal, A Java library to perform S-expansions of Lie algebras, arXiv:1703.04036 [INSPIRE].
[61] Inostroza, C.; Kondrashuk, I.; Merino, N.; Nadal, F., On the algorithm to find S-related Lie algebras, J. Phys. Conf. Ser., 1085 (2018)
[62] Bergshoeff, E.; Izquierdo, JM; Ortín, T.; Romano, L., Lie algebra expansions and actions for non-relativistic gravity, JHEP, 08, 048 (2019) · Zbl 1421.83128
[63] L. Romano, Non-relativistic four dimensional p-brane supersymmetric theories and Lie algebra expansion, arXiv:1906.08220 [INSPIRE].
[64] Fontanella, A.; Romano, L., Lie algebra expansion and integrability in superstring σ-models, JHEP, 07, 083 (2020) · Zbl 1451.83093
[65] Peñafiel, DM; Salgado-ReboLledó, P., Non-relativistic symmetries in three space-time dimensions and the Nappi-Witten algebra, Phys. Lett. B, 798, 135005 (2019) · Zbl 1460.81036
[66] Gomis, J.; Kleinschmidt, A.; Palmkvist, J.; Salgado-ReboLledó, P., Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity, JHEP, 02, 009 (2020) · Zbl 1435.83123
[67] Bergshoeff, E.; Gomis, J.; Salgado-ReboLledó, P., Non-relativistic limits and three-dimensional coadjoint Poincaré gravity, Proc. Roy. Soc. Lond. A, 476, 20200106 (2020) · Zbl 1472.83067
[68] Concha, P.; Ravera, L.; Rodríguez, E.; Rubio, G., Three-dimensional Maxwellian extended Newtonian gravity and flat limit, JHEP, 10, 181 (2020) · Zbl 1461.83005
[69] Izaurieta, F.; Rodriguez, E.; Minning, P.; Salgado, P.; Perez, A., Standard general relativity from Chern-Simons gravity, Phys. Lett. B, 678, 213 (2009)
[70] Diaz, J.; Fierro, O.; Izaurieta, F.; Merino, N.; Rodriguez, E.; Salgado, P., A generalized action for (2 + 1)-dimensional Chern-Simons gravity, J. Phys. A, 45, 255207 (2012) · Zbl 1246.83165
[71] Concha, PK; Peñafiel, DM; Rodríguez, EK; Salgado, P., Even-dimensional general relativity from Born-Infeld gravity, Phys. Lett. B, 725, 419 (2013) · Zbl 1364.83046
[72] 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. B728 (2014) 5 [INSPIRE]. · Zbl 1377.83103
[73] Caroca, R.; Concha, P.; Fierro, O.; Rodríguez, E.; Salgado-ReboLledó, P., Generalized Chern-Simons higher-spin gravity theories in three dimensions, Nucl. Phys. B, 934, 240 (2018) · Zbl 1395.83084
[74] Izaurieta, F.; Rodriguez, E.; Salgado, P., Eleven-dimensional gauge theory for the M algebra as an Abelian semigroup expansion of osp(32|1), Eur. Phys. J. C, 54, 675 (2008) · Zbl 1189.81199
[75] Fierro, O.; Izaurieta, F.; Salgado, P.; Valdivia, O., Minimal AdS-Lorentz supergravity in three-dimensions, Phys. Lett. B, 788, 198 (2019) · Zbl 1405.83072
[76] Concha, PK; Rodríguez, EK, N = 1 supergravity and Maxwell superalgebras, JHEP, 09, 090 (2014) · Zbl 1333.83221
[77] Concha, PK; Fierro, O.; Rodríguez, EK, Inönü-Wigner contraction and D = 2 + 1 supergravity, Eur. Phys. J. C, 77, 48 (2017)
[78] Banaudi, A.; Ravera, L., Generalized AdS-Lorentz deformed supergravity on a manifold with boundary, Eur. Phys. J. Plus, 133, 514 (2018)
[79] Concha, P.; Peñafiel, DM; Rodríguez, E., On the Maxwell supergravity and flat limit in 2 + 1 dimensions, Phys. Lett. B, 785, 247 (2018) · Zbl 1398.83121
[80] Caroca, R.; Concha, P.; Rodríguez, E.; Salgado-ReboLledó, P., Generalizing the bms_3and 2D-conformal algebras by expanding the Virasoro algebra, Eur. Phys. J. C, 78, 262 (2018)
[81] Caroca, R.; Concha, P.; Fierro, O.; Rodríguez, E., Three-dimensional Poincaré supergravity and N -extended supersymmetric BMS_3algebra, Phys. Lett. B, 792, 93 (2019) · Zbl 1416.83135
[82] Caroca, R.; Concha, P.; Fierro, O.; Rodríguez, E., On the supersymmetric extension of asymptotic symmetries in three spacetime dimensions, Eur. Phys. J. C, 80, 29 (2020)
[83] Nappi, CR; Witten, E., A WZW model based on a nonsemisimple group, Phys. Rev. Lett., 71, 3751 (1993) · Zbl 0972.81635
[84] Figueroa-O’Farrill, JM; Stanciu, S., More D-branes in the Nappi-Witten background, JHEP, 01, 024 (2000) · Zbl 0989.81091
[85] Inonu, E.; Wigner, EP, On the contraction of groups and their represenations, Proc. Nat. Acad. Sci., 39, 510 (1953) · Zbl 0050.02601
[86] Edelstein, JD; Hassaine, M.; Troncoso, R.; Zanelli, J., Lie-algebra expansions, Chern-Simons theories and the Einstein-Hilbert Lagrangian, Phys. Lett. B, 640, 278 (2006) · Zbl 1248.81115
[87] Schrader, R., The Maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys., 20, 701 (1972)
[88] 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. A67 (1970) 267 [INSPIRE]. · Zbl 0195.56002
[89] Gomis, J.; Kleinschmidt, A., On free Lie algebras and particles in electro-magnetic fields, JHEP, 07, 085 (2017) · Zbl 1380.83104
[90] Concha, PK; Rodríguez, EK, Maxwell superalgebras and Abelian semigroup expansion, Nucl. Phys. B, 886, 1128 (2014) · Zbl 1325.17002
[91] Aldrovandi, R.; Barbosa, AL; Crispino, LCB; Pereira, JG, Non-relativistic spacetimes with cosmological constant, Class. Quant. Grav., 16, 495 (1999) · Zbl 0934.83042
[92] Gibbons, GW; Patricot, CE, Newton-Hooke space-times, Hpp waves and the cosmological constant, Class. Quant. Grav., 20, 5225 (2003) · Zbl 1055.83009
[93] Brugues, J.; Gomis, J.; Kamimura, K., Newton-Hooke algebras, non-relativistic branes and generalized pp-wave metrics, Phys. Rev. D, 73 (2006)
[94] 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]. · Zbl 1119.83038
[95] Papageorgiou, G.; Schroers, BJ, Galilean quantum gravity with cosmological constant and the extended q-Heisenberg algebra, JHEP, 11, 020 (2010) · Zbl 1294.83029
[96] Duval, C.; Horvathy, P., Conformal Galilei groups, Veronese curves, and Newton-Hooke spacetimes, J. Phys. A, 44, 335203 (2011) · Zbl 1223.70060
[97] Hartong, J.; Lei, Y.; Obers, NA, Nonrelativistic Chern-Simons theories and three-dimensional Hořava-Lifshitz gravity, Phys. Rev. D, 94 (2016)
[98] Duval, C.; Gibbons, G.; Horvathy, P., Conformal and projective symmetries in Newtonian cosmology, J. Geom. Phys., 112, 197 (2017) · Zbl 1355.53067
[99] Howe, PS; Izquierdo, JM; Papadopoulos, G.; Townsend, PK, New supergravities with central charges and Killing spinors in (2 + 1)-dimensions, Nucl. Phys. B, 467, 183 (1996) · Zbl 1003.83518
[100] Giacomini, A.; Troncoso, R.; Willison, S., Three-dimensional supergravity reloaded, Class. Quant. Grav., 24, 2845 (2007) · Zbl 1117.83112
[101] Troncoso, R.; Zanelli, J., Higher dimensional gravity, propagating torsion and AdS gauge invariance, Class. Quant. Grav., 17, 4451 (2000) · Zbl 0979.83039
[102] Concha, PK; Peñafiel, DM; Rodríguez, EK; Salgado, P., Generalized Poincaré algebras and Lovelock-Cartan gravity theory, Phys. Lett. B, 742, 310 (2015) · Zbl 1345.83028
[103] Concha, PK; Durka, R.; Merino, N.; Rodríguez, EK, New family of Maxwell like algebras, Phys. Lett. B, 759, 507 (2016) · Zbl 1367.17023
[104] Afshar, HR; Bergshoeff, EA; Mehra, A.; Parekh, P.; Rollier, B., A Schrödinger approach to Newton-Cartan and Hořava-Lifshitz gravities, JHEP, 04, 145 (2016) · Zbl 1388.83003
[105] Pestun, V., Localization of gauge theory on a four-sphere and supersymmetric Wilson loops, Commun. Math. Phys., 313, 71 (2012) · Zbl 1257.81056
[106] Festuccia, G.; Seiberg, N., Rigid supersymmetric theories in curved superspace, JHEP, 06, 114 (2011) · Zbl 1298.81145
[107] Concha, P.; Ravera, L.; Rodríguez, E., Three-dimensional exotic Newtonian gravity with cosmological constant, Phys. Lett. B, 804, 135392 (2020) · Zbl 1435.83195
[108] Hansen, D.; Hartong, J.; Obers, NA, Action principle for Newtonian gravity, Phys. Rev. Lett., 122 (2019)
[109] Ravera, L., AdS Carroll Chern-Simons supergravity in 2 + 1 dimensions and its flat limit, Phys. Lett. B, 795, 331 (2019) · Zbl 1421.83137
[110] F. Ali and L. Ravera, \( \mathcal{N} \)-extended Chern-Simons Carrollian supergravities in 2 + 1 spacetime dimensions, JHEP02 (2020) 128 [arXiv:1912.04172] [INSPIRE]. · Zbl 1435.83191
[111] Ciambelli, L.; Marteau, C.; Petkou, AC; Petropoulos, PM; Siampos, K., Covariant Galilean versus Carrollian hydrodynamics from relativistic fluids, Class. Quant. Grav., 35, 165001 (2018) · Zbl 1409.83080
[112] Ciambelli, L.; Marteau, C.; Petkou, AC; Petropoulos, PM; Siampos, K., Flat holography and Carrollian fluids, JHEP, 07, 165 (2018) · Zbl 1395.81210
[113] Ciambelli, L.; Marteau, C., Carrollian conservation laws and Ricci-flat gravity, Class. Quant. Grav., 36 (2019) · Zbl 1476.83124
[114] Campoleoni, A.; Ciambelli, L.; Marteau, C.; Petropoulos, PM; Siampos, K., Two-dimensional fluids and their holographic duals, Nucl. Phys. B, 946, 114692 (2019) · Zbl 1430.81066
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.