World-manifold and target space anomalies in heterotic Green-Schwarz strings and five-branes

TL;DR

This paper investigates anomalies in heterotic string and five-brane theories, revealing discrepancies with duality expectations and analyzing anomaly cancellation conditions in a ten-dimensional background.

Contribution

It provides a detailed analysis of world-volume and target space anomalies in heterotic strings and five-branes, highlighting unexpected differences with duality conjectures.

Findings

World-volume anomalies cancel with 32 heterotic fermions for strings.

Five-brane anomalies cancel with only 16 heterotic fermions, contrary to expectations.

Target space anomaly polynomial for five-branes differs by a factor of 1/2 from duality predictions.

Abstract

The quantum consistency of sigma-models describing the dynamics of extended objects in a curved background requires the cancellation of their world-volume anomalies, which are conformal anomalies for the heterotic string and $SO(1,5)$ Lorentz-anomalies for the heterotic five-brane, and of their ten dimensional target space anomalies. In determining these anomalies in a $D=10$ Lorentz-covariant back-ground gauge we find that for the heterotic string the worldvolume anomalies cancel for 32 heterotic fermions while for the conjectured heterotic five-brane they cancel for only 16 heterotic fermions, this result being in contrast with the string/five-brane duality conjecture. For what concerns the target space anomalies we find that the five-brane eight-form Lorentz-anomaly polynomial differs by a factor of $1/2$ from what is expected on the basis of duality. Possible implications of these results are discussed.