High Energy Physics

I will describe how within eleven dimensional supergravity one can compute the logarithmic correction to the Bekenstein-Hawking entropy of certain magnetically charged asymptotically AdS_4 black holes with arbitrary horizon topology.  The result perfectly agrees with the dual field theory computation of the topologically twisted index in  ABJM theory and in certain theories obtained from M5 wrapping a hyperbolic 3-manifold. The extension to rotating, electrically charged AdS_4 black holes and the dual superconformal index will also be discussed. 

For any vertex operator algebra V, Y. Zhu constructed an associative algebra Zhu(V) that captures its representation theory (more generally, given a finite order automorphism g of V, there exists an algebra Zhu_g(V) that captures g-twisted representation theory of V). 

To a 4d N=2 superconformal theory T, one assigns a vertex algebra V[T] by the construction of Beem et al. We explain one role of Zhu algebra in this context. Namely, we show that a certain quotient of the Zhu algebra describes what happens to the Schur sector of the theory T under the dimensional reduction on S^1. This connects the VOA construction in 4d N=2 SCFT to the topological quantum mechanics construction in 3d N=4 SCFT, with the latter being given by the aforementioned quotient of the Zhu algebra. In the process, we will discuss how to reformulate the VOA construction on an S^3 x S^1 geometry.