A Curious Relation Between Gravity and Yang-Mills Theories

TL;DR

This paper reveals a formal connection between gravity in d dimensions and supersymmetric Yang-Mills theories in d+1 dimensions, suggesting a deep relation between these fundamental theories and their symmetries.

Contribution

It introduces a novel formalism expressing gravity as a restriction of higher-dimensional supersymmetric Yang-Mills theories with specific internal symmetries.

Findings

Gravity can be represented as a slice of higher-dimensional Yang-Mills theory.

Renormalization effects may contract internal symmetries to the Poincare group.

The approach links gravity and gauge theories through symmetry considerations.

Abstract

We find that Euclidian or Minkowski gravity in d dimensions can be formally expressed as the restriction to a slice of a supersymmetric Yang-Mills theory in d+1 dimensions with SO(d+1), SO(d,1) or SO(d-1,2) internal symmetry. We suggest that renormalization effects in the bulk imply a contraction of the latter symmetry into the Poincare group ISO(d) or ISO(d-1,1).