Vertex operator algebras, Higgs branches, and modular differential equations by Beem, C, Rastelli, L

“…In this work, we aim to characterize the connection between the Higgs branch of the moduli space of vacua (as an algebraic geometric entity) and the associated vertex operator algebra. Ultimately our proposal is simple, but its correctness requires the existence of a number of nontrivial null vectors in the vacuum Verma module of the vertex operator algebra. …”

Flavor symmetries and unitarity bounds in N = 2 superconformal field theories by Beem, C

“…I derive several general and far-reaching consequences of unitarity by computing the norms of flavor singlet Higgs branch operators appearing in the squares of “moment map” operators via the associated vertex operator algebra, and imposing the requirement that they be non-negative.…”

VOAs and rank-two instanton SCFTs by Beem, C, Meneghelli, C, Peelaers, W, Rastelli, L

“…We analyze the N=2 superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. …”

A geometric free field realisation for the genus-two class S theory of type a1 by Beem, C, Meneghelli, C

“…We present a free field realisation for the vertex operator algebra associated to the genus-two, class $\mathcal{S}$ superconformal field theory of type $\mathfrak{a}_1$. …”

Twisted chiral algebras of class S and mixed Feigin-Frenkel gluing by Beem, C, Nair, S

“…The correspondence between four-dimensional N=2 superconformal field theories and vertex operator algebras, when applied to theories of class S, leads to a rich family of VOAs that have been given the monicker chiral algebras of class S. …”

The SCFT/VOA correspondence for twisted class S by Nair, SS

“…A remarkably uniform construction of these vertex operator algebras has been put forward by Tomoyuki Arakawa in [Ara18]. …”

Free field realizations from the Higgs branch by Beem, C, Meneghelli, C, Rastelli, L

“…We present free field realizations for the associated vertex operator algebras of a number of four-dimensional N = 2 superconformal field theories. …”

Deformation Quantization and Superconformal Symmetry in Three Dimensions by Beem, C, Peelaers, W, Rastelli, L

“…We investigate the structure of certain protected operator algebras that arise in threedimensional N = 4 superconformal field theories. …”