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

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.

1+48 pages, v2:typo fixed+references added

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Cited by in corpus (9)

• Area-law versus Rényi and Tsallis black hole entropies
• Replica wormholes and capacity of entanglement
• Supersymmetric Rényi Entropy in Five Dimensions
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• Central Charges of 2d Superconformal Defects
• Topological pseudo entropy
• Holographic Line Defects in $D=4$, $N=2$ Gauged Supergravity
• Janus interface entropy and Calabi's diastasis in four-dimensional $\mathcal{N}=2$ superconformal field theories
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair