Gravitational interpretation of the Hitchin equations |
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Authors: | Gá bor Etesi |
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Affiliation: | Department of Geometry, Mathematical Institute, Faculty of Science, Budapest University of Technology and Economics, Egry J. u. 1, H ép., H-1111 Budapest, Hungary; Instituto de Matemática, Estatística e Computação Científica, Universidade Estadual de Campinas, C.P. 6065, 13083-859, Campinas, SP, Brazil |
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Abstract: | By referring to theorems of Donaldson and Hitchin, we exhibit a rigorous AdS/CFT-type correspondence between classical 2+1-dimensional vacuum general relativity theory on Σ×R and SO(3) Hitchin theory (regarded as a classical conformal field theory) on the spacelike past boundary Σ, a compact, oriented Riemann surface of genus greater than 1. Within this framework we can interpret the 2+1-dimensional vacuum Einstein equation as a decoupled “dual” version of the two-dimensional SO(3) Hitchin equations. |
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Keywords: | primary, 53C50 secondary, 58J10, 83E99 |
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