String Theory Journal Club

# Studying superconformal symmetry enhancement through indices

## by Mr. Mikhail Evtikhiev (Weizmann Institute)

Wednesday, September 19, 2018 from to (Europe/Berlin)
at SR3
 Description Many new non-Lagrangian superconformal field (SCF) theories have been found in the past few years. In some of the constructions it is not immediately obvious how many conserved supercharges does the theory have; e.g. a theory might be written in terms of d=4 N=1 SCF index yet possess N=2 supersymmetry (SUSY). In my talk, which is largely based on my paper 1708.08307, I will describe how one can study SCF symmetry enhancement in 3 to 6 dimensions using indices. Using N=1 d=4 case as an example, I will briefly discuss SCF algebra, SCF multiplets and shortening conditions, and introduce the notion of SCF index and respective equivalence classes. Then I will explain how conditions on index for SUSY enhancement arise, derive two simple conditions on N=1 -> N=2 SUSY enhancement in d=4 and describe the other conditions I managed to obtain. I will also demonstrate, how one can apply the derived conditions by proving, that several N=1 d=4 theories with rational central charges that might have had N=2 SUSY do not exhibit SUSY enhancement. If time permits, I will also briefly cover new developments on studying SUSY enhancement.