Abstract

Algebras of supersymmetry-protected local and extended operators can pro- vide an analytic window onto the structure of supersymmetric quantum field theories, even when they are strongly interacting. For example, 4d N = 2 SCF Ts have a sub- sector of local operators in the cohomology of a particular nilpotent supercharge which maps to a 2d vertex operator algebra (VOA), and certain surface operators in these theories correspond to non-vacuum modules of the VOA . In this talk, I will present a construction of extended operators residing in the cohomology of the VOA supercharge using the idea of topological descent. In doing so, I will show there exists a fascinating web of extended operators in every unitary 4d N = 2 SCFT which extends the structure furnished by the VOA . To demonstrate the richness of this extended operator algebra and its relation to the VOA , I will describe this construction for the simple case of a free hypermultiplet.