paper

A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime

arXiv:2210.10154 · doi:10.1007/JHEP02(2023)029

Abstract

We consider two BF formulations of the theory of gravity with a negative cosmological constant, of Plebanski and of MacDowell-Mansouri. Both give the standard Einstein equations in the bulk but differ in expressions of edge charges. We compute the asymptotic charges explicitly in both theories for AdS-Schwarzschild, AdS-Kerr, and AdS-Taub--NUT solutions. We find that while in the case of the Plebanski theory the charges are divergent, they are finite for MacDowell-Mansouri theory. Furthermore, we show that in the case of the arbitrary asymptotically AdS spacetimes, MacDowell--Mansouri asymptotic charges, action, and symplectic form are all finite. Therefore MacDowell-Mansouri theory of gravity in asymptotically AdS spaces does not need any counterterms.

22 pages, v2 (improved version prepared for publication with the extended supplement file and new references added)

References in corpus (18)