Target-space anomalies and elliptic indices in heterotic orbifolds

TL;DR

This paper analyzes mixed anomalies in heterotic Z_N orbifold models, showing they are encoded in an elliptic index and canceled via a universal Green-Schwarz mechanism, with a geometric interpretation involving torsion.

Contribution

It provides a complete string theory analysis of target-space anomalies in heterotic orbifolds, revealing their universal cancellation and geometric interpretation.

Findings

Anomalies are encoded in an elliptic index that can be computed easily.

Anomalies cancel through a universal Green-Schwarz mechanism involving the dilaton.

Target-space symmetry relates to torsion and affects the Green-Schwarz couplings.

Abstract

We present a complete string theory analysis of all mixed gauge, gravitational and target-space anomalies potentially arising in the simplest heterotic Z_N orbifold models, with N odd and standard embedding. These anomalies turn out to be encoded in an elliptic index, which can be easily computed; they are found to cancel through a universal GS mechanism induced by the dilaton multiplet. The target-space symmetry is then shown to have a nice geometric interpretation in terms of torsion, and the target-space dependence of the four-dimensional GS couplings can be alternatively rederived from the implicit torsion dependence of the standard ten-dimensional GS couplings. The result is universal and consists essentially of a Bianchi identity for the NSNS B field depending on all the curvatures, and in particular on the target-space curvature.