Quantum Field Theory and Physical Mathematics Seminar

Speaker: Mitch Weaver, KAIST

Title: The Extended Vertex Algebra of 4d N = 2 SCFTs and their Higher Products

Abstract: Every 4d N=2 superconformal field theory contains a BPS protected sub-algebra of local operators that has the structure of a vertex operator algebra (VOA). This VOA is identified by passing to the cohomology of a nilpotent supercharge, T, whose local operator cohomology is represented by twist-translated Schur operators with support in a Euclidean two-plane. When working in 4d Minkowski space, this cohomology admits a web of three extended operators (called descent operators) that are constructed from each Schur operator in the VOA, have worldvolume support in the Lorentzian two-plane that is transverse to the Euclidean plane supporting the VOA, and behave as point-like insertions in the plane of the VOA, i.e. as new chiral operators. The combined result is the extended vertex algebra (EVA): a universal extension of the VOA that canonically has the structure of a quasi-VOA, i.e. a vertex algebra (VA) with no conformal vector but which still possesses a representation of sl(2). After reviewing the VOA of Schur operators, I will explain the origin of the descent operators and present the OPEs for a subsector of the EVA in the free hyper SCFT.
Time permitting, I will also describe the construction and basic properties of a set of higher products that are associated to each descent operator. Such products function as higher dimensional versions of 2d chiral algebra λ-brackets, i.e. positive mode operators: they are defined on the EVA and map to the operators appearing in the singular terms of OPEs involving descent operators. Their existence offers a route toward sl(2) symmetry enhancement of the EVA and suggests the latter has structural properties that are common to the higher dimensional chiral algebras describing the minimal twists of 3d N = 2 and 4d N = 1 SQFTs. This talk is based on [2211.04410] and forthcoming work.