Webs of W-algebras
Tom\'a\v{s} Proch\'azka, Miroslav Rap\v{c}\'ak

TL;DR
This paper introduces a new framework for constructing and understanding vertex operator algebras using webs of interfaces in super Yang-Mills theory, connecting to known algebras and providing novel methods for algebra construction.
Contribution
It develops a gluing construction for Y-algebras associated with webs, generalizes $ ext{W}_{1+ ext{infinity}}$ algebra, and relates these to known VOAs through BRST and topological vertex methods.
Findings
Y-algebras are identified with truncations of $ ext{W}_{1+ ext{infinity}}$.
Gluing of Y-algebras reproduces counting of D-brane bound states.
Many classical VOAs are special cases of the new construction.
Abstract
We associate vertex operator algebras to -webs of interfaces in the topologically twisted super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of algebra. Starting with Y-algebras as atomic elements, we describe gluing of Y-algebras analogous to that of the topological vertex. At the level of characters, the construction matches the one of counting D0-D2-D4 bound states in toric Calabi-Yau threefolds. For some configurations of interfaces, we propose a BRST construction of the algebras and check in examples that both constructions agree. We define generalizations of algebra and identify a large class of glued algebras with their truncations. The gluing construction sheds new light on the structure of vertex operator algebras conventionally constructed by BRST…
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