Boundary Conditions in Topological AdS${}_4$/CFT${}_3$

Abstract

We revisit the construction in four-dimensional gauged $Spin(4)$ supergravity of the holographic duals to topologically twisted three-dimensional $\mathcal{N}=4$ field theories. Our focus in this paper is to highlight some subtleties related to preserving supersymmetry in AdS/CFT, namely the inclusion of finite counterterms and the necessity of a Legendre transformation to find the dual to the field theory generating functional. Studying the geometry of these supergravity solutions, we conclude that the gravitational free energy is indeed independent from the metric of the boundary, and it vanishes for any smooth solution.

37 pages

References in corpus (14)

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• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
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• Localization of the action in AdS/CFT
• Holographic renormalization and supersymmetry
• Supersymmetric Multi-trace Boundary Conditions in AdS
• Feynman diagrams and $\Omega$-deformed M-theory
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• Topological Chern-Simons Sigma Model
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• Twisted String Theory in Anti-de Sitter Space
• Pure and Twisted Holography
• Topological AdS/CFT and the $\Omega$ deformation