Speaker
Description
In this talk, we explore the important role played by polylogarithms in quantum field theory and string theory scattering amplitudes, along with the challenges in generalizing these functions beyond the realm of elliptic polylogarithms. As our main result, we will present a new construction of homotopy-invariant iterated integrals on a Riemann surface, applicable to any genus. Our method employs convolutions of the Arakelov Green function and holomorphic Abelian differentials to establish higher-genus equivalents of the genus-one integration kernels from the Kronecker-Eisenstein series. These kernels are combined into a flat connection, from which we build a homotopy-invariant, path-ordered exponential generating function. The coefficients of this generating function define higher-genus polylogarithms, which generalize the Brown-Levin construction beyond genus one. The resulting polylogarithms are expected to not only play a fundamental role in higher-genus computations of string amplitudes but to also find broad applications in various other areas of theoretical physics.
