Yang-Mills theory as a quantum gravity with `aether'

Abstract

Quantum Yang-Mills theory can be rewritten in terms of gauge-invariant variables: it has the form of the so-called BF gravity, with an additional `aether' term. The BF gravity based on the gauge group SU(N) is actually a theory of high spin fields (up to J=N) with high local symmetry mixing up fields with different spins -- like in supergravity but without fermions. At N going to infinity one gets a theory with an infinite tower of spins related by local symmetry, similar to what one has in string theory. We, thus, outline a way to derive string theory from a local Yang-Mills theory in the large N limit.