Two-dimensional conformal field theory, full vertex algebra and current-current deformation

Abstract

The main purpose of this paper is a mathematical construction of a non-perturbative deformation of a two-dimensional conformal field theory. We introduce a notion of a full vertex algebra which formulates a compact two-dimensional conformal field theory. Then, we construct a deformation family of a full vertex algebra which serves as a current-current deformation of conformal field theory in physics. The parameter space of the deformation is expressed as a double coset of an orthogonal group, a quotient of an orthogonal Grassmannian. As an application, we consider a deformation of chiral conformal field theories, vertex operator algebras. A current-current deformation of a "vertex operator algebra" may produce new vertex operator algebras. We give a formula for counting the number of the isomorphic classes of vertex operator algebras obtained in this way. We demonstrate it for some holomorphic vertex operator algebra of central charge $24$.

66 pages, 1 figure. In version 4, add several results and the order of the sections was changed. Adv. Math (2023)

References in corpus (3)

• Solving the 3d Ising Model with the Conformal Bootstrap II. c-Minimization and Precise Critical Exponents
• Quantum coordinate ring in WZW model and affine vertex algebra extensions
• Automorphism groups and uniqueness of holomorphic vertex operator algebras of central charge $24$

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• The BRST quantisation of chiral BMS-like field theories
• Non-Chiral Vertex Operator Algebra Associated To Lorentzian Lattices And Narain CFTs
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• A Geometric Classification of the Holomorphic Vertex Operator Algebras of Central Charge 24
• Beauty And The Beast Part 2: Apprehending The Missing Supercurrent