Vertex algebras at the corner

  title={Vertex algebras at the corner},
  author={Davide Gaiotto and Miroslav Rap{\vc}{\'a}k},
  journal={Journal of High Energy Physics},
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… 

Higgs and Coulomb branches from vertex operator algebras

A bstractWe formulate a conjectural relation between the category of line defects in topologically twisted 3d N$$ \mathcal{N} $$ = 4 supersymmetric quantum field theories and categories of modules

Truncations of W\infinity Algebras

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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We prove some conjectures about vertex algebras which emerge in gauge theory constructions associated to the geometric Langlands program. In particular, we present the conjectural kernel vertex

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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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A bstractWe introduce two mirror constructions of Vertex Operator Algebras associated to special boundary conditions in 3d N$$ \mathcal{N} $$ = 4 gauge theories. We conjecture various relations

Webs of W-algebras

A bstractWe associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted N=4$$ \mathcal{N}=4 $$ super Yang-Mills theory. Y-algebras associated to trivalent junctions

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

A BSTRACT . The universal two-parameter W ∞ -algebra is a classifying object for vertex algebras of type W (2 , 3 , . . . , N ) for some N . Gaiotto and Rapˇc´ak recently introduced a large family of

On extensions of gl (m )n ⏜ Kac-Moody algebras and Calabi-Yau singularities

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

Logarithmic W-algebras and Argyres-Douglas theories at higher rank

  • T. Creutzig
  • Mathematics
    Journal of High Energy Physics
  • 2018
A bstractFamilies of vertex algebras associated to nilpotent elements of simply-laced Lie algebras are constructed. These algebras are close cousins of logarithmic W-algebras of Feigin and Tipunin



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