N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole

TL;DR

This paper explores the holographic duality between four-dimensional N=4 super-Yang-Mills theories on conic spaces and five-dimensional STU topological black holes, showing protected universal contributions in free energy and supersymmetric Renyi entropy.

Contribution

It constructs supersymmetric theories on conic spaces with background R-symmetry fields and identifies their holographic duals as STU topological black holes, demonstrating exact agreement in key observables.

Findings

Universal free energy contribution is the same at weak and strong coupling.

Holographic duals are identified as five-dimensional STU topological black holes.

Perfect agreement between field theory and gravity results in the planar limit.

Abstract

We construct four-dimensional N=4 super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Renyi entropy using heat kernel method as well as localization technique. We find that the universal contribution to the partition function in the free field limit is the same as that in the strong coupling limit, which implies that it may be protected by supersymmetry. Based on the fact that, the conic sphere can be conformally mapped to $S^1\times H^3$ and the R-symmetry background fields can be supported by the R-charges of black hole, we propose that the holographic dual of these theories are five-dimensional, supersymmetric STU topological black holes. We demonstrate perfect agreement between N=4 super-Yang-Mills theories in the planar limit and the STU topological black holes.