Boundary Conditions in Topological AdS$_4$/CFT$_3$
Pietro Benetti Genolini, Matan Grinberg, Paul Richmond
TL;DR
This paper examines the subtle boundary conditions and supersymmetry preservation in four-dimensional gauged supergravity duals of topologically twisted 3D field theories, revealing that the gravitational free energy is boundary-metric independent and always zero.
Contribution
It clarifies the role of finite counterterms and Legendre transformations in maintaining supersymmetry in AdS/CFT for these models.
Findings
Gravitational free energy is boundary-metric independent.
Free energy vanishes for all smooth solutions.
Highlights subtleties in supersymmetry preservation.
Abstract
We revisit the construction in four-dimensional gauged supergravity of the holographic duals to topologically twisted three-dimensional 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.
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