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.
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Durka, R., Kowalski-Glikman, J. A tale of two theories of gravity in asymptotically Anti-de Sitter spacetime. J. High Energ. Phys. 2023, 29 (2023). https://doi.org/10.1007/JHEP02(2023)029
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DOI: https://doi.org/10.1007/JHEP02(2023)029