Topological AdS/CFT

Abstract

We define a holographic dual to the Donaldson-Witten topological twist of $\mathcal{N}=2$ gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to $\mathcal{N}=4$ gauged supergravity in five dimensions, with the four-manifold as conformal boundary. Under AdS/CFT, minus the logarithm of the partition function of the gauge theory is identified with the holographically renormalized supergravity action. We show that the latter is independent of the metric on the boundary four-manifold, as required for a topological theory. Supersymmetric solutions in the bulk satisfy first order differential equations for a twisted $Sp(1)$ structure, which extends the quaternionic Kahler structure that exists on any Riemannian four-manifold boundary. We comment on applications and extensions, including generalizations to other topological twists.

51 pages; further typos corrected

References in corpus (8)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The gravity duals of N=2 superconformal field theories
• Holographic renormalization and supersymmetry
• Supercurrent anomalies in 4d SCFTs
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• Euclidean Supergravity
• Trisecting non-Lagrangian theories
• The Boundary Multiplet of N=4 SU(2)xU(1) Gauged Supergravity on Asymptotically-AdS_5

Cited by in corpus (15)

• BRST quantization and equivariant cohomology: localization with asymptotic boundaries
• Twisting and localization in supergravity: equivariant cohomology of BPS black holes
• Holographic Surface Defects in $D=5$, $N=4$ Gauged Supergravity
• Supersymmetry anomalies in new minimal supergravity
• Superstrings in Thermal Anti-de Sitter Space
• Twisted holography of defect fusions
• Twisted String Theory in Anti-de Sitter Space
• The Holographic Dual of the $\Omega$-background
• Pure and Twisted Holography
• Gravitational free energy in topological AdS/CFT
• Topological AdS/CFT and the $\Omega$ deformation
• Correspondence between the twisted $N=2$ super-Yang-Mills and conformal Baulieu-Singer theories
• Boundary Conditions in Topological AdS${}_4$/CFT${}_3$
• Spontaneous symmetry breaking in a non-Abelian topological gauge theory
• Twisting BFSS & IKKT