Prochazka, Tomas; Rapcak, Miroslav
(2018):
Webs of Walgebras.
In: Journal of High Energy Physics, No. 11, 109

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Abstract
We associate vertex operator algebras to (p, q)webs of interfaces in the topologically twisted N = 4 super YangMills theory. Yalgebras associated to trivalent junctions are identified with truncations of W1+infinity algebra. Starting with Yalgebras as atomic elements, we describe gluing of Yalgebras analogous to that of the topological vertex. At the level of characters, the construction matches the one of counting D0D2D4 bound states in toric CalabiYau 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 W1+infinity 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 reductions or coset constructions and provides us with a way to construct new algebras. Many wellknown vertex operator algebras, such as U(N)(k) affine Lie algebra, N = 2 superconformal algebra, N = 2 superWinfinity, BershadskyPolyakov W3((2)), cosets and DrinfeldSokolov reductions of unitary groups can be obtained as special cases of this construction.