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|Type:||Artigo de periódico|
|Title:||Gravitational interpretation of the Hitchin equations|
|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 Sigma x R and SO(3) Hitchin theory (regarded as a classical conformal field theory) on the spacelike past boundary Sigma, 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. More precisely, we prove that if over Sigma with a fixed conformal class a real solution of the SO(3) Hitchin equations with induced flat SO(2, 1) connection is given, then there exists a certain cohomology class of non-isometric, singular, flat Lorentzian metrics on Sigma x R whose Levi-Civita connections are precisely the lifts of this induced flat connection and the conformal class induced by this cohomology class on Sigma agrees with the fixed one. Conversely, given a singular, flat Lorentzian metric on Sigma x R the restriction of its Levi-Civita connection gives rise to a real solution of the SO(3) Hitchin equations on Sigma with respect to the conformal class induced by the corresponding cohomology class of the Lorentzian metric. (c) 2007 Elsevier B.V. All rights reserved.|
2+1-dimensional general relativity
|Editor:||Elsevier Science Bv|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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