Abstract
We define and study a holographic dual to the topological twist of \( \mathcal{N}=4 \) gauge theories on Riemannian three-manifolds. The gravity duals are solutions to four-dimensional \( \mathcal{N}=4 \) gauged supergravity, where the three-manifold arises as a conformal boundary. Following our previous work, we show that the renormalized gravitational free energy of such solutions is independent of the boundary three-metric, as required for a topological theory. We then go further, analyzing the geometry of supersymmetric bulk solutions. Remarkably, we are able to show that the gravitational free energy of any smooth four-manifold filling of any three-manifold is always zero. Aided by this analysis, we prove a similar result for topological AdS5/CFT4. We comment on the implications of these results for the large N limits of topologically twisted gauge theories in three and four dimensions, including the ABJM theory and \( \mathcal{N}=4 \) SU(N) super-Yang-Mills, respectively.
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Genolini, P.B., Richmond, P. & Sparks, J. Gravitational free energy in topological AdS/CFT. J. High Energ. Phys. 2018, 100 (2018). https://doi.org/10.1007/JHEP09(2018)100
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DOI: https://doi.org/10.1007/JHEP09(2018)100