# Vertex algebras at the corner

@article{Gaiotto2019VertexAA, title={Vertex algebras at the corner}, author={Davide Gaiotto and Miroslav Rap{\vc}{\'a}k}, journal={Journal of High Energy Physics}, year={2019}, volume={2019}, pages={1-88} }

A bstractWe introduce a class of Vertex Operator Algebras which arise at junctions of supersymmetric interfaces in N$$ \mathcal{N} $$ = 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 YL,M,N, which…

## 107 Citations

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We introduce a new class of Vertex Operator Algebras Y+ and their duals, which generalize the standard W-algebras WN of type sl(N). These algebras can be defined in terms of junctions of boundary…

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### Orbifolds of Gaiotto-Rap\v{c}\'ak $Y$-algebras

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We discuss a class of vertex operator algebras Wm|n×∞ generated by a supermatrix of fields for each integral spin 1, 2, 3, . . . . The algebras admit a large family of truncations that are in…

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