The Ten-dimensional Effective Action of Strongly Coupled Heterotic String Theory

TL;DR

This paper derives the ten-dimensional effective action for strongly coupled heterotic string theory from M-theory, incorporating heavy modes and ensuring anomaly cancellation, thus extending understanding of non-perturbative string dynamics.

Contribution

It introduces a method to derive the effective action by integrating out heavy modes, providing a complete set of higher-order terms consistent with supersymmetry and anomaly cancellation.

Findings

Derived the complete ten-dimensional effective action including R^4, F^2R^2, and F^4 terms.

Confirmed the effective action matches weakly coupled one-loop results.

Illustrated the integration of heavy modes in theories with dynamical boundaries.

Abstract

We derive the ten-dimensional effective action of the strongly coupled heterotic string as the low energy limit of M-theory on S^1/Z_2. In contrast to a conventional dimensional reduction, it is necessary to integrate out nontrivial heavy modes which arise from the sources located on the orbifold fixed hyperplanes. This procedure, characteristic of theories with dynamical boundaries, is illustrated by a simple example. Using this method, we determine a complete set of R^4, F^2R^2, and F^4 terms and the corresponding Chern-Simons and Green-Schwarz terms in ten dimensions. As required by anomaly cancelation and supersymmetry, these terms are found to exactly coincide with their weakly coupled one-loop counterparts.