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Operator algebra

About: Operator algebra is a research topic. Over the lifetime, 5783 publications have been published within this topic receiving 165303 citations.


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TL;DR: In this paper, the authors associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted super Yang-Mills theory and identify vertices associated to trivalent junctions with truncations of a 1+∞ algebra.
Abstract: We associate vertex operator algebras to (p, q)-webs of interfaces in the topologically twisted $$ \mathcal{N}=4 $$ super Yang-Mills theory. Y-algebras associated to trivalent junctions are identified with truncations of $$ \mathcal{W} $$ 1+∞ 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 $$ \mathcal{W} $$ 1+∞ 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 well-known vertex operator algebras, such as U(N)k affine Lie algebra, $$ \mathcal{N}=2 $$ superconformal algebra, $$ \mathcal{N}=2 $$ super- $$ {\mathcal{W}}_{\infty } $$ , Bershadsky-Polyakov $$ {\mathcal{W}}_3^{(2)} $$ , cosets and Drinfeld-Sokolov reductions of unitary groups can be obtained as special cases of this construction.

54 citations

Journal ArticleDOI
TL;DR: In this paper, the authors analyzed the vertex operator algebra of superconformal field theories and showed that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group.
Abstract: We analyze the $$\mathcal {N}=2$$ superconformal field theories that arise when a pair of D3-branes probe an F-theory singularity from the perspective of the associated vertex operator algebra. We identify these vertex operator algebras for all cases; we find that they have a completely uniform description, parameterized by the dual Coxeter number of the corresponding global symmetry group. We further present free field realizations for these algebras in the style of recent work by three of the authors. These realizations transparently reflect the algebraic structure of the Higgs branches of these theories. We find fourth-order linear modular differential equations for the vacuum characters/Schur indices of these theories, which are again uniform across the full family of theories and parameterized by the dual Coxeter number. We comment briefly on expectations for the still higher-rank cases.

54 citations

Journal ArticleDOI
TL;DR: In this article, the Toda lattice hierarchy is discussed in connection with the topological description of the c = 1 string theory compactified at the self-dual radius.

54 citations

Journal ArticleDOI
TL;DR: In this paper, it was shown that the graded trace functions arising from the Conway group's action on the canonically twisted module are constant in the case of Leech lattice automorphisms with fixed points and are principal moduli for genus-zero groups.
Abstract: We exhibit an action of Conway’s group – the automorphism group of the Leech lattice – on a distinguished super vertex operator algebra, and we prove that the associated graded trace functions are normalized principal moduli, all having vanishing constant terms in their Fourier expansion. Thus we construct the natural analogue of the Frenkel–Lepowsky–Meurman moonshine module for Conway’s group. The super vertex operator algebra we consider admits a natural characterization, in direct analogy with that conjectured to hold for the moonshine module vertex operator algebra. It also admits a unique canonically twisted module, and the action of the Conway group naturally extends. We prove a special case of generalized moonshine for the Conway group, by showing that the graded trace functions arising from its action on the canonically twisted module are constant in the case of Leech lattice automorphisms with fixed points, and are principal moduli for genus-zero groups otherwise.

54 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202337
202277
2021125
2020141
2019173
2018169