Worldvolume and target space anomalies in the D=10 super--fivebrane sigma--model

TL;DR

The paper calculates anomalies in a proposed ten-dimensional super-fivebrane model, finding a discrepancy with duality expectations that suggests the model's heterotic sector must include more fermions for consistency.

Contribution

It provides the first detailed one-loop anomaly calculation for the heterotic super-fivebrane sigma-model, revealing a mismatch with duality predictions and implications for the model's fermionic content.

Findings

Anomalies are half of what duality predicts.

Worldvolume anomaly cancels with 16 Weyl fermions.

Implication that the heterotic sector needs more fermions.

Abstract

The fields of the conjectured ``heterotic" super--fivebrane sigma--model in ten dimensions are made out of a well known gravitational sector, the $X$ and the $\vartheta$, and of a still unknown heterotic sector which should be coupled to the Yang--Mills fields. We compute the one--loop $d=6$ worldvolume and $D=10$ target space Lorentz--anomalies which arise from the gravitational sector of the heterotic super--fivebrane sigma--model, using a method which we developed previously for the Green--Schwarz heterotic superstring. These anomalies turn out to carry an overall coefficient which is $1/2$ of that required by the string/fivebrane duality conjecture. As a consequence the worldvolume anomaly vanishes if the heterotic fields consist of 16 (rather than 32) complex Weyl fermions on the worldvolume. This implies that the string/fivebrane duality conjecture can not be based on a ``heterotic" super--fivebrane sigma--model with only fermions in the heterotic sector. Possible implications of this result are discussed.