Abstract
In this work, we apply the semigroup expansion method of Lie algebras to construct novel and known three-dimensional hypergravity theories. We show that the expansion procedure considered here yields a consistent way of coupling different three-dimensional Chern-Simons gravity theories with massless spin-\( \frac{5}{2} \) gauge fields. First, by expanding the \( \mathfrak{osp} \)(1|4) superalgebra with a particular semigroup a generalized hyper-Poincaré algebra is found. Interestingly, the hyper-Poincaré and hyper-Maxwell algebras appear as subalgebras of this generalized hypersymmetry algebra. Then, we show that the generalized hyper-Poincaré CS gravity action can be written as a sum of diverse hypergravity CS Lagrangians. We extend our study to a generalized hyper-AdS gravity theory by considering a different semigroup. Both generalized hyperalgebras are then found to be related through an Inönü-Wigner contraction which can be seen as a generalization of the existing vanishing cosmological constant limit between the hyper-AdS and hyper-Poincaré gravity theories.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
C. Aragone and S. Deser, Hypersymmetry in D = 3 of Coupled Gravity Massless Spin 5/2 System, Class. Quant. Grav. 1 (1984) L9 [INSPIRE].
M.A. Vasiliev, Extended Higher Spin Superalgebras and Their Realizations in Terms of Quantum Operators, Fortsch. Phys. 36 (1988) 33 [INSPIRE].
M.P. Blencowe, A Consistent Interacting Massless Higher Spin Field Theory in D = (2 + 1), Class. Quant. Grav. 6 (1989) 443 [INSPIRE].
E. Bergshoeff, M.P. Blencowe and K.S. Stelle, Area Preserving Diffeomorphisms and Higher Spin Algebra, Commun. Math. Phys. 128 (1990) 213 [INSPIRE].
M.A. Vasiliev, Higher spin gauge theories in four-dimensions, three-dimensions, and two-dimensions, Int. J. Mod. Phys. D 5 (1996) 763 [hep-th/9611024] [INSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [INSPIRE].
E.S. Fradkin and M.A. Vasiliev, On the Gravitational Interaction of Massless Higher Spin Fields, Phys. Lett. B 189 (1987) 89 [INSPIRE].
M.A. Vasiliev, Consistent equation for interacting gauge fields of all spins in (3 + 1)-dimensions, Phys. Lett. B 243 (1990) 378 [INSPIRE].
M.A. Vasiliev, Nonlinear equations for symmetric massless higher spin fields in (A)dS(d), Phys. Lett. B 567 (2003) 139 [hep-th/0304049] [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].
M. Henneaux, G. Lucena Gómez, J. Park and S.-J. Rey, Super- W(infinity) Asymptotic Symmetry of Higher-Spin AdS3 Supergravity, JHEP 06 (2012) 037 [arXiv:1203.5152] [INSPIRE].
A. Achucarro and P.K. Townsend, Extended Supergravities in d = (2 + 1) as Chern-Simons Theories, Phys. Lett. B 229 (1989) 383 [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].
Y.M. Zinoviev, Hypergravity in AdS3, Phys. Lett. B 739 (2014) 106 [arXiv:1408.2912] [INSPIRE].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Extended anti-de Sitter Hypergravity in 2 + 1 Dimensions and Hypersymmetry Bounds, in the proceedings of the International Workshop on Higher Spin Gauge Theories, Singapore Singapore, November 4–6 (2017), p. 139–157 [https://doi.org/10.1142/9789813144101_0009] [arXiv:1512.08603] [INSPIRE].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Hypersymmetry bounds and three-dimensional higher-spin black holes, JHEP 08 (2015) 021 [arXiv:1506.01847] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Extension of the Poincaré group with half-integer spin generators: hypergravity and beyond, JHEP 09 (2015) 003 [arXiv:1505.06173] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotically flat structure of hypergravity in three spacetime dimensions, JHEP 10 (2015) 009 [arXiv:1508.04663] [INSPIRE].
R. Caroca et al., Hypersymmetric extensions of Maxwell-Chern-Simons gravity in 2 + 1 dimensions, Phys. Rev. D 104 (2021) 064011 [arXiv:2105.12243] [INSPIRE].
H. Bacry, P. Combe and J.L. Richard, Group-theoretical analysis of elementary particles in an external electromagnetic field. I. the relativistic particle in a constant and uniform field, Nuovo Cim. A 67 (1970) 267 [INSPIRE].
H. Bacry, P. Combe and J.L. Richard, Group-theoretical analysis of elementary particles in an external electromagnetic field. II. the nonrelativistic particle in a constant and uniform field, Nuovo Cim. A 70 (1970) 289 [INSPIRE].
R. Schrader, The maxwell group and the quantum theory of particles in classical homogeneous electromagnetic fields, Fortsch. Phys. 20 (1972) 701 [INSPIRE].
J. Gomis and A. Kleinschmidt, On free Lie algebras and particles in electro-magnetic fields, JHEP 07 (2017) 085 [arXiv:1705.05854] [INSPIRE].
D. Cangemi, One formulation for both lineal gravities through a dimensional reduction, Phys. Lett. B 297 (1992) 261 [gr-qc/9207004] [INSPIRE].
C. Duval, Z. Horvath and P.A. Horvathy, Chern-Simons gravity, based on a non-semisimple group, arXiv:0807.0977 [INSPIRE].
J. Gomis, K. Kamimura and J. Lukierski, Deformations of Maxwell algebra and their Dynamical Realizations, JHEP 08 (2009) 039 [arXiv:0906.4464] [INSPIRE].
S. Bonanos, J. Gomis, K. Kamimura and J. Lukierski, Deformations of Maxwell Superalgebras and Their Applications, J. Math. Phys. 51 (2010) 102301 [arXiv:1005.3714] [INSPIRE].
R. Durka, J. Kowalski-Glikman and M. Szczachor, Gauged AdS-Maxwell algebra and gravity, Mod. Phys. Lett. A 26 (2011) 2689 [arXiv:1107.4728] [INSPIRE].
J.A. de Azcárraga, K. Kamimura and J. Lukierski, Maxwell symmetries and some applications, Int. J. Mod. Phys. Conf. Ser. 23 (2013) 01160 [arXiv:1201.2850] [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].
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].
L. Avilés et al., Non-Relativistic Maxwell Chern-Simons Gravity, JHEP 05 (2018) 047 [arXiv:1802.08453] [INSPIRE].
P. Concha et al., 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].
P. Salgado-Rebolledo, The Maxwell group in 2 + 1 dimensions and its infinite-dimensional enhancements, JHEP 10 (2019) 039 [arXiv:1905.09421] [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. Adami, P. Concha, E. Rodríguez and H.R. Safari, Asymptotic symmetries of Maxwell Chern-Simons gravity with torsion, Eur. Phys. J. C 80 (2020) 967 [arXiv:2005.07690] [INSPIRE].
S. Kibaroğlu and O. Cebecioğlu, Gauge theory of the Maxwell and semi-simple extended (anti) de Sitter algebra, Int. J. Mod. Phys. D 30 (2021) 2150075 [arXiv:2007.14795] [INSPIRE].
P. Concha, D. Peñafiel, L. Ravera and E. Rodríguez, Three-dimensional Maxwellian Carroll gravity theory and the cosmological constant, Phys. Lett. B 823 (2021) 136735 [arXiv:2107.05716] [INSPIRE].
O. Cebecioğlu, A. Saban and S. Kibaroğlu, Maxwell extension of f(R) gravity, Eur. Phys. J. C 83 (2023) 95 [arXiv:2210.09454] [INSPIRE].
J.A. de Azcárraga, K. Kamimura and J. Lukierski, Generalized cosmological term from Maxwell symmetries, Phys. Rev. D 83 (2011) 124036 [arXiv:1012.4402] [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) 310o [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].
R. Caroca et al., Generalized Chern-Simons higher-spin gravity theories in three dimensions, Nucl. Phys. B 934 (2018) 240 [arXiv:1712.09975] [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].
F. Izaurieta, P. Salgado and R. Salgado, Einstein-Chern-Simons equations on the 3-brane world, Nucl. Phys. B 980 (2022) 115832 [arXiv:2105.00532] [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 et al., 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. Peñafiel, E.K. Rodríguez 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 et al., Pure Lovelock gravity and Chern-Simons theory, Phys. Rev. D 94 (2016) 024055 [arXiv:1603.09424] [INSPIRE].
M.M.A. Paixão and O. Piguet, Five dimensional Chern-Simons gravity for the expanded (anti)-de Sitter gauge group C5, Eur. Phys. J. C 80 (2020) 138 [arXiv:1912.06634] [INSPIRE].
L. Cardenas, J. Diaz, P. Salgado and D. Salgado, Generalized Einstein gravities and generalized AdS symmetries, Nucl. Phys. B 984 (2022) 115943 [arXiv:2208.06107] [INSPIRE].
P. Salgado and S. Salgado, \( \mathfrak{so} \)(D − 1, 1) ⨂ \( \mathfrak{so} \)(D − 1, 2) algebras and gravity, Phys. Lett. B 728 (2014) 5 [INSPIRE].
P.K. Concha, N. Merino and E.K. Rodríguez, 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].
D.V. Soroka and V.A. Soroka, Tensor extension of the Poincaré algebra, Phys. Lett. B 607 (2005) 302 [hep-th/0410012] [INSPIRE].
H. Bacry and J. Levy-Leblond, Possible kinematics, J. Math. Phys. 9 (1968) 1605 [INSPIRE].
A. Ashtekar, J. Bicak and B.G. Schmidt, Asymptotic structure of symmetry reduced general relativity, Phys. Rev. D 55 (1997) 669 [gr-qc/9608042] [INSPIRE].
G. Barnich and G. Compere, Classical central extension for asymptotic symmetries at null infinity in three spacetime dimensions, Class. Quant. Grav. 24 (2007) F15 [gr-qc/0610130] [INSPIRE].
C. Duval, G.W. Gibbons and P.A. Horvathy, Conformal Carroll groups and BMS symmetry, Class. Quant. Grav. 31 (2014) 092001 [arXiv:1402.5894] [INSPIRE].
P. Concha et al., 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. Inönu and E.P. Wigner, On the Contraction of groups and their represenations, Proc. Nat. Acad. Sci. 39 (1953) 510 [INSPIRE].
E.J. Saletan, Contraction of Lie Groups, J. Math. Phys. 2 (1961) 1.
E. Weimar-Woods, Contractions of Lie algebras: Generalized Inönü–Wigner contractions versus graded contractions, J. Math. Phys. 36 (1995) 4519.
M. Gerstenhaber, On the Deformation of Rings and Algebras, Annals Math. 79 (1963) 59 [INSPIRE].
A. Nijenhuis and R.W. Richardson Jr., Cohomology and deformations in graded Lie algebras, Bull. Am. Math. Soc. 72 (1966) 1.
A. Fialowski, On Deformations and Contractions of Lie Algebras, SIGMA 2 (2006) 048.
J.A. de Azcárraga, J.M. Izquierdo, M. Picon and O. Varela, Extensions, expansions, Lie algebra cohomology and enlarged superspaces, Class. Quant. Grav. 21 (2004) S1375 [hep-th/0401033] [INSPIRE].
A. Medina and P. Revoy, Algèbres de Lie et produit scalaire invariant, Annales Sci. Ecole Norm. Sup. 18 (1985) 553.
J.M. Figueroa-O’Farrill and S. Stanciu, On the structure of symmetric selfdual Lie algebras, J. Math. Phys. 37 (1996) 4121 [hep-th/9506152] [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].
M. Hatsuda and M. Sakaguchi, Wess-Zumino term for the AdS superstring and generalized Inönu-Wigner contraction, Prog. Theor. Phys. 109 (2003) 853 [hep-th/0106114] [INSPIRE].
J.A. de Azcárraga, 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. B 662 (2003) 185 [hep-th/0212347] [INSPIRE].
F. Izaurieta, E. Rodríguez and P. Salgado, Expanding Lie (super)algebras through Abelian semigroups, J. Math. Phys. 47 (2006) 123512 [hep-th/0606215] [INSPIRE].
J.A. de Azcárraga, J.M. Izquierdo, M. Picon and O. Varela, Expansions of algebras and superalgebras and some applications, Int. J. Theor. Phys. 46 (2007) 2738 [hep-th/0703017] [INSPIRE].
F. Izaurieta, E. Rodríguez and P. Salgado, Eleven-dimensional gauge theory for the M algebra as an Abelian semigroup expansion of \( \mathfrak{osp} \)(32|1), Eur. Phys. J. C 54 (2008) 675 [hep-th/0606225] [INSPIRE].
J.A. de Azcárraga, J.M. Izquierdo, J. Lukierski and M. Woronowicz, Generalizations of Maxwell (super)algebras by the expansion method, Nucl. Phys. B 869 (2013) 303 [arXiv:1210.1117] [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, E.K. Rodríguez and P. Salgado, Generalized supersymmetric cosmological term in N = 1 Supergravity, JHEP 08 (2015) 009 [arXiv:1504.01898] [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].
D.M. Peñafiel and P. Salgado-Rebolledo, 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-Rebolledo, Newton-Hooke/Carrollian expansions of (A)dS and Chern-Simons gravity, JHEP 02 (2020) 009 [arXiv:1912.07564] [INSPIRE].
A. Fontanella and L. Romano, Lie Algebra Expansion and Integrability in Superstring Sigma-Models, JHEP 07 (2020) 083 [arXiv:2005.01736] [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].
P. Concha, M. Ipinza, L. Ravera and E. Rodríguez, Non-relativistic three-dimensional supergravity theories and semigroup expansion method, JHEP 02 (2021) 094 [arXiv:2010.01216] [INSPIRE].
O. Kasikci and M. Ozkan, Lie algebra expansions, non-relativistic matter multiplets and actions, JHEP 01 (2022) 081 [arXiv:2111.14568] [INSPIRE].
J. Gomis and A. Kleinschmidt, Infinite-Dimensional Algebras as Extensions of Kinematic Algebras, Front. in Phys. 10 (2022) 892812 [arXiv:2202.05026] [INSPIRE].
R. Caroca, D.M. Peñafiel and P. Salgado-Rebolledo, Nonrelativistic spin-3 symmetries in 2+1 dimensions from expanded and extended Nappi-Witten algebras, Phys. Rev. D 107 (2023) 064034 [arXiv:2208.00602] [INSPIRE].
R. Caroca, P. Concha, E. Rodríguez and P. Salgado-Rebolledo, 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 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].
M. Banados, R. Troncoso and J. Zanelli, Higher dimensional Chern-Simons supergravity, Phys. Rev. D 54 (1996) 2605 [gr-qc/9601003] [INSPIRE].
S. Bonanos, J. Gomis, K. Kamimura and J. Lukierski, Maxwell Superalgebra and Superparticle in Constant Gauge Badkgrounds, Phys. Rev. Lett. 104 (2010) 090401 [arXiv:0911.5072] [INSPIRE].
J.A. de Azcárraga and J.M. Izquierdo, Minimal D = 4 supergravity from the superMaxwell algebra, Nucl. Phys. B 885 (2014) 34 [arXiv:1403.4128] [INSPIRE].
P. Concha, L. Ravera and E. Rodríguez, Three-dimensional Maxwellian extended Bargmann supergravity, JHEP 04 (2020) 051 [arXiv:1912.09477] [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].
J. Diaz et al., A generalized action for (2 + 1)-dimensional Chern-Simons gravity, J. Phys. A 45 (2012) 255207 [arXiv:1311.2215] [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].
M. Henneaux, A. Pérez, D. Tempo and R. Troncoso, Chemical potentials in three-dimensional higher spin anti-de Sitter gravity, JHEP 12 (2013) 048 [arXiv:1309.4362] [INSPIRE].
C. Bunster et al., Generalized Black Holes in Three-dimensional Spacetime, JHEP 05 (2014) 031 [arXiv:1404.3305] [INSPIRE].
O. Coussaert and M. Henneaux, Supersymmetry of the (2 + 1) black holes, Phys. Rev. Lett. 72 (1994) 183 [hep-th/9310194] [INSPIRE].
G. Barnich, L. Donnay, J. Matulich and R. Troncoso, Asymptotic symmetries and dynamics of three-dimensional flat supergravity, JHEP 08 (2014) 071 [arXiv:1407.4275] [INSPIRE].
O. Fuentealba, J. Matulich and R. Troncoso, Asymptotic structure of \( \mathcal{N} \) = 2 supergravity in 3D: extended super-BMS3 and nonlinear energy bounds, JHEP 09 (2017) 030 [arXiv:1706.07542] [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].
P. Concha, C. Henríquez-Báez and E. Rodríguez, Non-relativistic and ultra-relativistic expansions of three-dimensional spin-3 gravity theories, JHEP 10 (2022) 155 [arXiv:2208.01013] [INSPIRE].
P. Concha, J. Matulich, L. Ravera and E. Rodríguez, Three-dimensional extended Bargmann hypergravity. FT-UAM/CSIC-23-46.
Acknowledgments
This work was partially supported by the National Agency for Research and Development ANID - FONDECYT grants No. 1211077, 11220328, 1181031, 1221624, 1211226, 11220486 and SIA grant No. SA77210097. R.C. would like to thank to the Universidad Arturo Prat, Playa Brava 3265, 1111346, Iquique, Chile, for their support. P.C. and E.R. would like to thank to the Dirección de Investigación and Vicerectoría de Investigación of the Universidad Católica de la Santísima Concepción, Chile, for their constant support. J.M. has been supported by the MCI, AEI, FEDER (UE) grants PID2021-125700NB-C21 (“Gravity, Supergravity and Superstrings” (GRASS)) and IFT Centro de Excelencia Severo Ochoa CEX2020-001007-S.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2304.10624
Rights and permissions
Open Access . This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Caroca, R., Concha, P., Matulich, J. et al. Three-dimensional hypergravity theories and semigroup expansion method. J. High Energ. Phys. 2023, 215 (2023). https://doi.org/10.1007/JHEP08(2023)215
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP08(2023)215