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

TL;DR

This paper demonstrates that certain AKSZ-Manin deformations of topological gauge theories in 2-4 dimensions are equivalent to gravitational theories, revealing a deep connection between topological field theories and gravity.

Contribution

It establishes a novel link between AKSZ-Manin theories and gravity, showing equivalences in multiple dimensions, including a new derivation of 4D Einstein gravity from AKSZ deformations.

Findings

2D and 3D gravity are topological and require background sources.

4D Einstein gravity is obtained via AKSZ-Manin deformation.

The approach unifies gauge and gravitational theories through topological methods.

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.