2017/07/31 by Pietro Benetti Genolini, Paul Richmond, James Sparks
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary (topology) #Combinatorics #Cosmology and Gravitation Theories #Curvature #Gauge theory #Gauged supergravity #Hermitian manifold #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Orbifold #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum mechanics #Ricci curvature #Riemannian manifold #Supergravity #Supersymmetry #Topological quantum field theory #Topology (electrical circuits) #hep-th #math.DG
paper · pdf · doi:10.1007/jhep12(2017)039
published as JHEP 1712 (2017) 039 · 51 pages; further typos corrected
openalex publication_date 2017/12/01 · arxiv created 2019/07/29 · arxiv updated 2019/07/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We define a holographic dual to the Donaldson-Witten topological twist of N=2 gauge theories on a Riemannian four-manifold. This is described by a class of asymptotically locally hyperbolic solutions to 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 Kähler structure that exists on any Riemannian four-manifold boundary. We comment on applications and extensions, including generalizations to other topological twists.