Abstract

Any N = 2 superconformal field theory (SCFT) in four dimensions has a sector of operators related to a two-dimensional chiral algebra containing a Virasoro sub-algebra. Moreover, there are well-known examples of isolated SCF Ts whose chiral algebra is a Virasoro algebra. In this talk, I will consider the chiral algebras associated with interacting N = 2 SCF Ts possessing an exactly marginal deformation that can be interpreted as a gauge coupling (i.e., at special points on the resulting conformal manifolds, free gauge fields appear that decouple from isolated SCFT building blocks). At any point on these conformal manifolds, I will argue that the associated chiral algebras possess at least three generators. In addition, I will show that there are examples of SCF Ts realizing such a minimal chiral algebra: they are certain points on the conformal manifold obtained by considering the low-energy limit of type IIB string theory on a particular three complex-dimensional hyper surface singularity I will describe. The associated chiral algebra is the A(6) theory of Feigin, Feigin, and Tipunin. As byproducts of this discussion, I will argue that (i) a collection of isolated theories can be conformally gauged only if there is a SUSY moduli space associated with the corresponding symmetry current moment maps in each sector, and (ii) N = 2 SCF Ts with a ≥ c have hidden fermionic symmetries (in the sense of fermionic chiral algebra generators).