Dyonic Anomalies

TL;DR

This paper explores the complex coupling of dyonic p-branes to higher-form fields in specific dimensions, highlighting the construction of a coupling functional and the associated anomaly related to the brane's normal bundle.

Contribution

It explicitly constructs a coupling functional for p=1 branes, incorporating a Wess-Zumino term and analyzing the anomaly related to the Euler class.

Findings

Constructed a coupling functional for p=1 branes.

Identified the anomaly related to the Euler class.

Showed the functional's well-definedness depends on anomaly cancellation.

Abstract

We consider the problem of coupling a dyonic p-brane in d = 2p+4 space-time dimensions to a prescribed (p+2)-form field strength. This is particularly subtle when p is odd. For the case p = 1, we explicitly construct a coupling functional, which is a sum of two terms: one which is linear in the prescribed field strength, and one which describes the coupling of the brane to its self-field and takes the form of a Wess-Zumino term depending only on the embedding of the brane world-volume into space-time. We then show that this functional is well-defined only modulo a certain anomaly, related to the Euler class of the normal bundle of the brane world-volume.