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Theses

Topological holography

Songyuan Li 1, 2
2 Champs, Gravitation et Cordes
LPENS (UMR_8023) - Laboratoire de physique de l'ENS - ENS Paris
Abstract : This thesis concentrates on the topologically twisted version of the AdS₃/CFT₂ correspondence. We start by studying the topologically twisted N=2 supersymmetric Liouville theory with massive deformations. We determine the chiral ring elements and compute their correlations functions. We then turn to define a three-dimensional gravity theory that is the holographic dual of Liouville theory. The action of this gravity theory is the same as the one of classical general relativity while the path integral measure is taken to be the same as the Liouville theory. We study in detail the properties of this gravity theory and then generalize it to the supersymmetric case where by changing the boundary conditions we find it dual to the topologically twisted N=2 supersymmetric Liouville theory mentioned above. The classical configurations corresponding to the chiral ring will be computed. Next, we turn to a string realization of the duality and analyze a string theory on the locally AdS₃ background with a conformally flat boundary. We find the boundary energy-momentum tensor becomes topological when we impose a specific coupling to the boundary metric given by the boundary conditions. Finally, we study the topological orbifold conformal field theories on the symmetric product of a complex surface M, which is the conjectured dual to the ten-dimensional string theory on AdS₃×S³×M.
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Submitted on : Thursday, June 24, 2021 - 10:52:13 AM
Last modification on : Tuesday, July 13, 2021 - 3:29:41 AM

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  • HAL Id : tel-03269600, version 1

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Songyuan Li. Topological holography. Physics [physics]. Université Paris sciences et lettres, 2020. English. ⟨NNT : 2020UPSLE018⟩. ⟨tel-03269600⟩

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