Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions

Details Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions

2003-05-20

arxiv.org/abs/hep-th/0305168v1

Phys.Rev. D70 (2004) 045017

Physics

High Energy Physics

High Energy Physics - Theory

Scientific paper

10.1103/PhysRevD.70.045017

We argue that two dimensional classical SU(2) Yang-Mills theory describes the embedding of Riemann surfaces in three dimensional curved manifolds. Specifically, the Yang-Mills field strength tensor computes the Riemannian curvature tensor of the ambient space in a thin neighborhood of the surface. In this sense the two dimensional gauge theory then serves as a source of three dimensional gravity. In particular, if the three dimensional manifold is flat it corresponds to the vacuum of the Yang-Mills theory. This implies that all solutions to the original Gauss-Codazzi surface equations determine two dimensional integrable models with a SU(2) Lax pair. Furthermore, the three dimensional SU(2) Chern-Simons theory describes the Hamiltonian dynamics of two dimensional Riemann surfaces in a four dimensional flat space-time.

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