Spin-3 fields in Mielke-Baekler gravity

Abstract

Mielke-Baekler gravity consists in the usual Einstein-Hilbert action with a cosmological term and rotational and translational Chern-Simons terms with arbitrary couplings. For a particular choice of these couplings, we can obtain Einstein-Hilbert action, its teleparallel equivalent, and the exotic Witten's gravity.In this work, we use the Chern-Simons formalism to generalize the three dimensional Mielke-Baekler gravity theory in order to introduce spin-3 fields. We study its asymptotic symmetries, black hole solution, and also analyse its canonical structure at its singular point.

Non-relativistic limit of the Mielke–Baekler gravity theory

“…One could expect that the extended Bargmann supergravity [50], the extended Newton-Hooke [73] and the recent NR teleparallel supergravity [63] appear for particular values of the ( p, q) parameters. In the higher-spin case, one could start by exploring the NR limit of the spin-3 MB gravity theory studied in [24] and check if the spin-3 extended Bargmann gravity introduced in [76,77] appears as a particular subcase. Then, after considering the limit ξ → ∞ in (2.1), the NR generators satisfy the following commutation relations: (5.3)…”

“…Thus, the MB gravity is a useful toy model to study and analyze the role of the torsion and curvature in the AdS/CFT correspondence [11]. Different issues about the MB gravity were explored in [12][13][14][15][16][17][18][19][20][21][22][23][24][25][26], such as its relation with the Chern-Simons (CS) action, black hole solutions, asymptotic symmetries, holography, its supersymmetric extension and its coupling to higher-spin gauge fields.…”