Vertex algebras at the corner

Abstract

We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N = 4 Super Yang Mills gauge theory. These vertex algebras satisfy non-trivial duality relations inherited from S-duality of the four-dimensional gauge theory. The gauge theory construction equips the vertex algebras with collections of modules labelled by supersymmetric interface line defects. We discuss in detail the simplest class of algebras Y L,M,N , which generalizes W N algebras. We uncover tantalizing relations between Y L,M,N , the topological vertex and the W 1+∞ algebra.

Abelian dualities of $$ \mathcal{N} $$ = (0, 4) boundary conditions

“…N for 3d hypermultiplet so that it is compatible with the H-twist (mirror Rozansky-Witten twist). The resulting deformed boundary condition supports the VOA Sb of symplectic bosons X(z) and Y (z) of conformal dimension 1 2 which obey the OPE [39,36]…”

Higgs and Coulomb branches from vertex operator algebras

“…There are various intertwined relations between supersymmetric gauge theories and Vertex Operator Algebras [1][2][3][4][5][6][7][8][9][10][11]. In many of these constructions the VOA emerges as the local operator algebra of some QFT which is topological away from some special two-dimensional location or defect and holomorphic at the defect.…”

Instanton R-matrix and $$ \mathcal{W} $$-symmetry

“…There is a nice combinatorial description of the truncation in terms of plane partitions (box-counting) which is discussed in [72,73]. The free field representation of Y N 1 ,N 2 ,N 3 was constructed in [67].…”