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Energy bounds for vertex operator algebra extensions
Let V be a simple unitary vertex operator algebra and U be a (polynomially) energy-bounded unitary subalgebra containing the conformal vector of V ....
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Product-Type Classes for Vertex Algebra Cohomology of Foliations on Complex Curves
We introduce the vertex algebra cohomology of foliations on complex curves. Generalizing the classical case, the orthogonality condition with respect...
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Graphical Calculus for Quantum Vertex Operators, I: The Dynamical Fusion Operator
This paper is the first in a series on graphical calculus for quantum vertex operators. We establish in great detail the foundations of graphical...
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Logarithmic Vertex Algebras and Non-local Poisson Vertex Algebras
Logarithmic vertex algebras were introduced in our previous paper, motivated by logarithmic conformal field theory (Bakalov and Villarreal in...
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Superspace expansion of the 11D linearized superfields in the pure spinor formalism, and the covariant vertex operator
11D pure spinors have been shown to successfully describe 11D supergravity in a manifestly super-Poincaré covariant manner. The feasibility of its...
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Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24
We describe the automorphism groups of all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one Lie algebras by...
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First cohomologies of affine, Virasoro, and lattice vertex operator algebras
In this paper, we study the first cohomologies for the following three examples of vertex operator algebras: (i) the simple affine VOA associated...
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Unitary forms for holomorphic vertex operator algebras of central charge 24
We prove that all holomorphic vertex operator algebras of central charge 24 with non-trivial weight one subspaces are unitary. The main method is to...
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On the commutant of the principal subalgebra in the \(A_1\) lattice vertex algebra
The coset (commutant) construction is a fundamental tool to construct vertex operator algebras from known vertex operator algebras. The aim of this...
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Reconstruction of Vertex Algebras in Even Higher Dimensions
Vertex algebras in higher dimensions correspond to models of quantum field theory with global conformal invariance. Any vertex algebra in dimension D ...
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Vertex operator algebras and topologically twisted Chern-Simons-matter theories
We consider several topologically twisted Chern-Simons-matter theories and propose boundary VOAs whose module categories should model the category of...
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Unitary Vertex Algebras and Wightman Conformal Field Theories
We prove an equivalence between the following notions: (i) unitary Möbius vertex algebras, and (ii) Wightman conformal field theories on the circle...
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Limits of Vertex Algebras and Large N Factorization
We investigate the limit of sequences of vertex algebras. We discuss under what condition the vector space direct limit of such a sequence is again a...