Recording of the online particle physics theory seminar by Oliver Schlotterer (University of Uppsala)
Abstract:
This talk is dedicated to mathematical structures in the low-energy expansion of
one-loop string amplitudes. I will review basics of string perturbation theory and
give examples of connections with number theory from the integration over moduli
of punctured worldsheet. At one loop, the insertion of external states on the open-
and closed-string worldsheets requires integration over punctures on a cylinder
boundary and a torus, respectively. Suitable bases of such integrals will be shown
to obey simple first-order differential equations in the modular parameter of the
surface. These differential equations will be exploited to perform the integrals
order by order in the inverse string tension, similar to modern strategies for
dimensionally regulated Feynman integrals. Our method manifests the appearance
of iterated integrals over holomorphic Eisenstein series in the low-energy expansion.
Moreover, infinite families of Laplace equations can be generated for the modular
forms in closed-string low-energy expansions.