Two-loop Euler-Heisenberg effective actions from charged open strings

TL;DR

This paper derives the two-loop Euler-Heisenberg effective action for adjoint scalars in a gauge field background using open string theory, providing a string-based approach to multiloop quantum field calculations.

Contribution

It introduces a multiloop open string partition function with a constant gauge field, connecting string theory computations to field theory effective actions at two loops.

Findings

Derived the multiloop partition function in the presence of a gauge field.

Explicit representation of twisted determinants on higher-genus Riemann surfaces.

Recovered the two-loop Euler-Heisenberg effective action from string theory.

Abstract

We present the multiloop partition function of open bosonic string theory in the presence of a constant gauge field strength, and discuss its low-energy limit. The result is written in terms of twisted determinants and differentials on higher-genus Riemann surfaces, for which we provide an explicit representation in the Schottky parametrization. In the field theory limit, we recover from the string formula the two-loop Euler-Heisenberg effective action for adjoint scalars minimally coupled to the background gauge field.