Cyclic products of higher-genus Szegö kernels, modular tensors and polylogarithms
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866908360940453888 |
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| author | D'Hoker, Eric Hidding, Martijn Schlotterer, Oliver |
| author_facet | D'Hoker, Eric Hidding, Martijn Schlotterer, Oliver |
| contents | A wealth of information on multiloop string amplitudes is encoded in fermionic two-point functions known as Szegö kernels. In this paper we show that cyclic products of any number of Szegö kernels on a Riemann surface of arbitrary genus may be decomposed into linear combinations of modular tensors on moduli space that carry all the dependence on the spin structure $δ$. The $δ$-independent coefficients in these combinations carry all the dependence on the marked points and are composed of the integration kernels of higher-genus polylogarithms. We determine the antiholomorphic moduli derivatives of the $δ$-dependent modular tensors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_05044 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Cyclic products of higher-genus Szegö kernels, modular tensors and polylogarithms D'Hoker, Eric Hidding, Martijn Schlotterer, Oliver High Energy Physics - Theory Algebraic Geometry Number Theory A wealth of information on multiloop string amplitudes is encoded in fermionic two-point functions known as Szegö kernels. In this paper we show that cyclic products of any number of Szegö kernels on a Riemann surface of arbitrary genus may be decomposed into linear combinations of modular tensors on moduli space that carry all the dependence on the spin structure $δ$. The $δ$-independent coefficients in these combinations carry all the dependence on the marked points and are composed of the integration kernels of higher-genus polylogarithms. We determine the antiholomorphic moduli derivatives of the $δ$-dependent modular tensors. |
| title | Cyclic products of higher-genus Szegö kernels, modular tensors and polylogarithms |
| topic | High Energy Physics - Theory Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2308.05044 |