YANG--MILLS THEORY IN THREE DIMENSIONS AS A QUANTUM GRAVITY THEORY
Diakonov D., Petrov V.

Received: May 31, 2000

PACS: 11.15.Ha, 12.38.Gc

We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but is embedded into a flat 6-dimensional space (for the SU(2) gauge group). In the continuum limit, the theory can be reformulated in terms of 6-component gauge-invariant scalar fields having the meaning of the external coordinates of the dual lattice sites. These 6-component fields induce a metric and a curvature of the 3-dimensional dual color space. The Yang-Mills theory can be identically rewritten as a quantum gravity theory with the Einstein-Hilbert action but a purely imaginary Newton constant, plus a homogeneous «ether» term. The theory can be formulated in a gauge-invariant and local form without explicit color degrees of freedom.