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Cyclic Products of Higher-Genus Szegö Kernels, Modular Tensors, and Polylogarithms
Eric D'Hoker1, Martijn Hidding2, Oliver Schlotterer2
1Mani L. Bhaumik Institute for Theoretical Physics, Department of Physics and Astronomy, <a href="https://ror.org/046rm7j60">University of California</a>, Los Angeles, California 90095, USA.
Abstract:
A wealth of information on multiloop string amplitudes is encoded in fermionic two-point functions known as Szegö kernels. Here 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.
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