Vertex Algebras at the Corner

Abstract

We introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in $\mathcal{N}=4$ 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 $W_{1+\infty }$ algebra.

102 pages, 22 figures. v2: corrected minor typos and updated references

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• On $W$-representations of $\beta$- and $q,t$-deformed matrix models
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• Twisted compactifications of 3d N = 4 theories and conformal blocks
• Masses, Sheets and Rigid SCFTs