Yang-Mills origin of gravitational symmetries

TL;DR

This paper demonstrates that gravitational symmetries can be derived from Yang-Mills theories by viewing gravity as a convolution of left and right Yang-Mills fields combined with a scalar spectator, revealing a deep connection between gauge theories and gravity.

Contribution

It provides a novel derivation of gravitational symmetries from Yang-Mills symmetries using a convolution framework, specifically deriving supergravity symmetries from flat space Yang-Mills theories.

Findings

Derived gravitational symmetries from Yang-Mills symmetries in linear approximation.

Connected supergravity symmetries to flat space Yang-Mills gauge invariances.

Illustrated the approach with a specific supergravity example.

Abstract

By regarding gravity as the convolution of left and right Yang-Mills theories together with a spectator scalar field in the bi-adjoint representation, we derive in linearised approximation the gravitational symmetries of general covariance, p-form gauge invariance, local Lorentz invariance and local supersymmetry from the flat space Yang-Mills symmetries of local gauge invariance and global super-Poincar\'e. As a concrete example we focus on the new-minimal (12+12) off-shell version of simple four-dimensional supergravity obtained by tensoring the off-shell Yang-Mills multiplets (4+4,N_L =1)and(3+0,N_R =0).