Convergence and operadic compatibility of bulk and boundary OPEs in two-dimensional conformal field theory
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914603314708480 |
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| author | Moriwaki, Yuto |
| author_facet | Moriwaki, Yuto |
| contents | We prove convergence and compatibility of iterated bulk and boundary operator product expansions (OPEs) in two-dimensional conformal field theory with locally $C_1$-cofinite chiral symmetry. For each tree, we give an explicit domain of convergence for the corresponding iterated OPE. These local expansions glue to single-valued real analytic functions on the configuration spaces, which are the correlation functions of the theory. The proof uses an action of the parenthesized permutation-braid operad on $C_1$-cofinite module categories of a vertex operator algebra. This operad models the fundamental groupoid of the two-dimensional Swiss-cheese operad, and under this action the operadic generators correspond to the genus-zero bootstrap equations of boundary CFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_02648 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Convergence and operadic compatibility of bulk and boundary OPEs in two-dimensional conformal field theory Moriwaki, Yuto Quantum Algebra High Energy Physics - Theory Mathematical Physics We prove convergence and compatibility of iterated bulk and boundary operator product expansions (OPEs) in two-dimensional conformal field theory with locally $C_1$-cofinite chiral symmetry. For each tree, we give an explicit domain of convergence for the corresponding iterated OPE. These local expansions glue to single-valued real analytic functions on the configuration spaces, which are the correlation functions of the theory. The proof uses an action of the parenthesized permutation-braid operad on $C_1$-cofinite module categories of a vertex operator algebra. This operad models the fundamental groupoid of the two-dimensional Swiss-cheese operad, and under this action the operadic generators correspond to the genus-zero bootstrap equations of boundary CFT. |
| title | Convergence and operadic compatibility of bulk and boundary OPEs in two-dimensional conformal field theory |
| topic | Quantum Algebra High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2410.02648 |