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| Main Author: | |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2309.07528 |
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| _version_ | 1866916324928651264 |
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| author | Liu, Xun |
| author_facet | Liu, Xun |
| contents | We propose a method to challenge the calculation of genus-$g$, bulk $n$-point, $b$-boundary, $c$-crosscap correlation functions with $x$ boundary operators $\mathcal{F}_{g,n,b,c}^{x}$ in two-dimensional conformal field theories (CFT$_2$). We show that $\mathcal{F}_{g,n,b,c}^{x}$ are infinite linear combinations of genus-$g$, bulk $(n+b+c)$-point functions $\mathcal{F}_{g,(n+b+c)}$, and try to obtain the linear coefficients in this work. We show the existence of a single pole structure in the linear coefficients at degenerate limits. A practical method to obtain the infinite linear coefficients is the free field realizations of Ishibashi states. We review the results in Virasoro minimal models $\mathcal{M}(p,p')$ and extend it to the $N=1$ minimal models $\mathcal{SM}(p,p')$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_07528 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The linear property of genus-$g$, $n$-point, $b$-boundary, $c$-crosscap correlation functions in two-dimensional conformal field theory Liu, Xun High Energy Physics - Theory We propose a method to challenge the calculation of genus-$g$, bulk $n$-point, $b$-boundary, $c$-crosscap correlation functions with $x$ boundary operators $\mathcal{F}_{g,n,b,c}^{x}$ in two-dimensional conformal field theories (CFT$_2$). We show that $\mathcal{F}_{g,n,b,c}^{x}$ are infinite linear combinations of genus-$g$, bulk $(n+b+c)$-point functions $\mathcal{F}_{g,(n+b+c)}$, and try to obtain the linear coefficients in this work. We show the existence of a single pole structure in the linear coefficients at degenerate limits. A practical method to obtain the infinite linear coefficients is the free field realizations of Ishibashi states. We review the results in Virasoro minimal models $\mathcal{M}(p,p')$ and extend it to the $N=1$ minimal models $\mathcal{SM}(p,p')$. |
| title | The linear property of genus-$g$, $n$-point, $b$-boundary, $c$-crosscap correlation functions in two-dimensional conformal field theory |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2309.07528 |