Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions
Niemi, Antti J.
arXiv, 0305168 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2003-05-20
Classification:  High Energy Physics - Theory,  General Relativity and Quantum Cosmology,  Mathematical Physics,  Mathematics - Differential Geometry,  Mathematics - Dynamical Systems,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0305168,
     author = {Niemi, Antti J.},
     title = {Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0305168}
}

Niemi, Antti J. Three Dimensional Gravity From SU(2) Yang-Mills Theory in Two Dimensions. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0305168/