N = 4 $$ \mathcal{N}=4 $$ Super-Yang-Mills on conic space as hologram of STU topological black hole

We construct four-dimensional N = 4 $$ \mathcal{N}=4 $$ super-Yang-Mills theories on a conic sphere with various background R-symmetry gauge fields. We study free energy and supersymmetric Rényi 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 × ℍ 3 $$ {\mathbb{S}}^1\times {\mathrm{\mathbb{H}}}^3 $$ 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 $$ \mathcal{N}=4 $$ super-Yang-MillstheoriesintheplanarlimitandtheSTUtopologicalblackholes