Joint Theory Seminar by Oliver Schlotterer

Non-holomorphic modular forms and single-valued elliptic polylogarithms from strings

I will give an overview of the classes of functions or periods arising in the configuration-space integrals of string amplitudes. At genus one, open strings naturally realize elliptic polylogarithms and elliptic multiple zeta values while the integrals over torus worldsheets in closed-string amplitudes feature non-holomorphic modular forms. The latter are known as (elliptic) modular graph forms, and I will introduce canonical representations via iterated integrals over holomorphic modular forms and their complex conjugates. Elliptic modular graph forms can be viewed as generalizations of Zagier’s single-valued elliptic polylogarithms beyond depth one.