Gravity from AKSZ-Manin theories in two, three, and four dimensions

Abstract

We show that various dynamical gauge theories in two, three and four dimensions, obtained as Manin deformations of topological Alexandrov-Kontsevich-Schwarz-Zaboronsky (AKSZ) theories, are equivalent to gravitational theories. Since gravity is topological in two and three dimension, this equivalence requires a diffeomorphism breaking background source term. In four dimensions, however, the MacDowell-Mansouri formulation of Einstein gravity with a cosmological constant is obtained identically via the Manin deformation of a particular AKSZ theory.

17 pages. Published version with references and related commentary added. Minor typos corrected

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Cited by in corpus (1)

• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group