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.
Highlights
The rigid supersymmetry of gauge theories in curved backgrounds allows us to compute exact results of a certain class of BPS observables, for instance, the partition function of four-dimensional N = 2 theories in the Omega background [1] and on a round foursphere [2]
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 S1 × H3 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
Summary
The authors of [23] studied N ≥ 2 Chern-Simons matter theory on the q-branched three-sphere S3q with certain background vector fields turned on to maintain rigid supersymmetry They computed the supersymmetric partition function, with which a quantity called supersymmetric Renyi entropy ( SRE) is defined. Partition function can be computed exactly using localization technique and the result is valid for general N = 2 theories In this case we will see that the field theory on S4q shares interesting feature with that on a squashed four-sphere [10], the former was motivated by computing supersymmetric Renyi entropy while the latter was motivated by Alday-Gaiotto-Tachikawa (AGT) correspondence. We perform the heat kernel computation in the free field limit and find that the q-dependence remains exactly the same
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
