Three-dimensional extended Lifshitz, Schrödinger and Newton-Hooke supergravity

Abstract

We provide a systematic analysis of three-dimensional N = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schrödinger extensions. These algebras admit invariant non-degenerate bi-linear forms which we utilized to construct corresponding Chern-Simons supergravity actions.

Oddity in nonrelativistic, strong gravity

“…We will take a slightly different -but equivalent -approach than the one that was previously taken in [1][2][3][4]. We will perform the expansion not directly in terms of the relativistic metric as in (23), but rather expand the components as obtained after a Newton-Cartan split as in (20), see also Table 1. It should be stressed that the Newton-Cartan structure τ μ , h μν is taken to be independent of c.…”

“…The work on the large c expansion, which by construction provides a nonrelativistic gravity theory descendant from GR, is also of value to the recent explorations of more general theories of nonrelativistic gravity. In that context we can mention for example recent work on 3d nonrelativistic gravity [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27], Lifshitz Holography [28][29][30][31], nonrelativistic string theory [32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47] and condensed matter and fluid mechanics applications [48][49][50][51][52][53][54][55][56][57]. In parallel the symmetries underlying such theories have been further investigated …”

Three-dimensional Maxwellian extended Bargmann supergravity

“…Three-dimensional non-relativistic (NR) and ultra-relativistic (UR) versions of supergravity theory have only been explored recently in [1][2][3][4][5][6][7]. Although several generalizations and applications of supergravity have been developed by diverse authors these last four decades, its NR construction remains challenging and has only been approached in three spacetime dimensions.…”

Lie algebra expansion and integrability in superstring Sigma-models

“…Lie algebra expansion has been also further extended to the semigroup expansion method [45][46][47][48][49]. These methods have recently found interesting applications in several different contexts [50][51][52][53][54].…”