Two-dimensional conformal field theory, full vertex algebra and current-current deformation
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arXiv
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866917740043829248 |
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| author | Moriwaki, Yuto |
| author_facet | Moriwaki, Yuto |
| contents | 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 $24$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_07327 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Two-dimensional conformal field theory, full vertex algebra and current-current deformation Moriwaki, Yuto Quantum Algebra Mathematical Physics 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 $24$. |
| title | Two-dimensional conformal field theory, full vertex algebra and current-current deformation |
| topic | Quantum Algebra Mathematical Physics |
| url | https://arxiv.org/abs/2007.07327 |