Boundary conditions in topological AdS4/CFT3

We revisit the construction in four-dimensional gauged Spin(4) supergravity of the holographic duals to topologically twisted three-dimensional 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.

Automated summary

This paper revisits the construction of holographic duals to topologically twisted three-dimensional N = 4 field theories in four-dimensional gauged Spin(4) supergravity, highlighting subtleties related to preserving supersymmetry in AdS/CFT. By studying the geometry of these supergravity solutions, it is concluded that the gravitational free energy is independent of the boundary metric and vanishes for any smooth solution.