Three dimensional gravity from SU(2) Yang-Mills theory in two dimensions
2004 (English)In: Phys. Rev., Vol. D70, 045017- p.Article in journal (Refereed) Published
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.
Place, publisher, year, edition, pages
2004. Vol. D70, 045017- p.
IdentifiersURN: urn:nbn:se:uu:diva-20928OAI: oai:DiVA.org:uu-20928DiVA: diva2:48701