Gravity duals of supersymmetric gauge theories on three-manifolds

Abstract

We study gravity duals to a broad class of N=2 supersymmetric gauge theories defined on a general class of three-manifold geometries. The gravity backgrounds are based on Euclidean self-dual solutions to four-dimensional gauged supergravity. As well as constructing new examples, we prove in general that for solutions defined on the four-ball the gravitational free energy depends only on the supersymmetric Killing vector, finding a simple closed formula when the solution has U(1) x U(1) symmetry. Our result agrees with the large N limit of the free energy of the dual gauge theory, computed using localization. This constitutes an exact check of the gauge/gravity correspondence for a very broad class of gauge theories with a large N limit, defined on a general class of background three-manifold geometries.

74 pages, 2 figures; v2: minor changes

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• The Unreasonable Effectiveness of Higher-Derivative Supergravity in AdS${}_4$ Holography
• Localization of the action in AdS/CFT
• Holographic renormalization and supersymmetry
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• The F-Theorem and F-Maximization
• Mass Deformations of the ABJM Theory: The Holographic Free Energy
• Maximally symmetric nuts in 4d $\mathcal{N}=2$ higher derivative supergravity
• NUTs, Bolts, and Spindles
• Harmonic forms on asymptotically AdS metrics
• Wrapped $M5$-branes and complex saddle points