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Two-dimensional quantum gravity coupled to non-conformal matter

Abstract : Finding a theory of quantum gravity describing in a consistent way the quantum properties of matter and spacetime geometry is one of the greatest challenges of modern theoretical physics. However after several decades of research, many conceptual and technical issues are still to be resolved. Insights on these questions can be given by simplified toy models that allow for exact computations. The first part of the thesis deals with two-dimensional quantum gravity. In two dimensions quantum gravity is much better understood and many computations can be carried out exactly. Whereas two-dimensional quantum gravity coupled to conformal matter has been widely studied and is now well understood, much less was known until recently when matter is non-conformal. First we compute the gravitational action for a massive scalar field on a Riemann surface with boundaries and then for a massive Majorana fermion on a manifold without boundary. The latter case corresponds to a CFT perturbed by a conformal perturbation and is usually tackled through the DDK ansatz, but the results do not seem to match. Finally we give a minisuperspace computation of the spectrum of the Mabuchi action, a functional that appears in the gravitational action for a massive scalar field. In the second part we focus on black hole thermal behaviour which provides a lot of insight of how a theory of quantum gravity should look like. In the context of string theory the AdS/CFT correspondence provides powerful tools for understanding the microscopic origin of black holes thermodynamics. We construct a quantum mechanical toy model based on holographic principles to study the dynamics of quantum black holes.
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  • HAL Id : tel-01706737, version 1

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Corinne de Lacroix de Lavalette. Two-dimensional quantum gravity coupled to non-conformal matter. Quantum Physics [quant-ph]. Université Pierre et Marie Curie - Paris VI, 2017. English. ⟨NNT : 2017PA066288⟩. ⟨tel-01706737⟩

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