Dirac Branes, Characteristic Currents and Anomaly Cancellations in 5-Branes

TL;DR

This paper explores anomaly cancellation in 5-branes using generalized Dirac branes, characteristic currents, and the PST formalism, providing a framework applicable to heterotic string theory and M5-branes.

Contribution

It introduces a geometric regularization of Dirac branes and applies the formalism to anomaly cancellation in supergravity theories involving 5-branes.

Findings

Anomaly inflow is automatically generated in heterotic string 5-brane theory.

Framework successfully addresses anomaly cancellation in specific supergravity models.

Identifies open problems related to Dirac anomalies in M5-brane theories.

Abstract

The aim of this note is to discuss, in a somewhat informal language, the cancellation of anomalies (in topologically trivial space-time) for 5-branes using as "building blocks": i) a generalization to p-branes of the Dirac strings of monopoles (Dirac branes) and a refinement of this idea involving a geometric regularization of Dirac branes, leading to the formalism of "characteristic currents" ii) the PST formalism . As an example of the potentiality of the developed framework we discuss in some detail the anomaly cancellation in the D=10 effective theory of heterotic string and 5-brane coupled to supergravity, where the anomaly inflow is automatically generated. Some remarks are also made on a similar approach to the problem of anomaly cancellation in the effective theory of M5-brane coupled to D=11 supergravity, developed in collaboration with M.Tonin, where however still as open problem remains a Dirac anomaly.