We present a new gauging of maximal supergravity in five spacetime dimensions with gauge group containing ISO(5), involving the local scaling symmetry of the metric, and admitting a supersym- metric anti-de Sitter vacuum. We show this maximal supergravity to arise by consistent truncation of M-theory on the (non-spherical, non-parallelisable) six-dimensional geometry associated to a stack of N M5-branes wrapped on a smooth Riemann surface. The existence of this truncation allows us to holographically determine the complete, universal spectrum of light operators of the dual four- dimensional N = 2 theory of class S. We then compute holographically the superconformal index of the dual field theory at large-N, finding perfect agreement with previously known field theory results in specific limits.

We formulate a two-sided Guionnet–Jones–Shlyakhtenko-like construction for a subfactor planar algebra $P$ to define two sequences of tracial, unital associative algebras which we show are isomorphic and on completing which, we obtain a sequence $M^k$ of von Neumann algebras. Further, when $P$ is the planar algebra of a finite group, we employ free probability techniques to explicitly identify $M^1$ and $M^2$ as interpolated free group factors.

In this talk, I will discuss about the structure of ideals in enveloping algebras of affine Kac-Moody algebras and explain a proof of the result which states that if U(L) is the enveloping algebra of the affine Lie algebra L and "c" is the central element of L, then any proper quotient of U(L)/(c) by two sided ideals has finite GK dimension and also talk about the applications of the result including the fact that U(L)/(c-$\lambda$) for non zero $\lambda$ is simple and annihilators of irreducible integrable highest weight modules over affine Lie algebras are centrally generated extending the earlier known result in case of Verma modules. This talk is based on joint work with Susan J. Sierra.