Dirac Quantisation Conditions and Kaluza-Klein Reduction

TL;DR

This paper derives the Dirac quantisation condition for p-brane charges in supergravity, showing its consistency with lower-dimensional theories and determining the universal charge lattice for BPS states.

Contribution

It establishes the form of the Dirac quantisation condition for supergravity p-branes and links it with Kaluza-Klein reduction, defining a universal charge lattice for BPS states.

Findings

Quantisation condition matches lower-dimensional results

Charge lattice is universal and modulus-independent

Ensures consistency of supergravity charges under dimensional reduction

Abstract

We present the form of the Dirac quantisation condition for the p-form charges carried by p-brane solutions of supergravity theories. This condition agrees precisely with the conditions obtained in lower dimensions, as is necessary for consistency with Kaluza-klein dimensional reduction. These considerations also determine the charge lattice of BPS soliton states, which proves to be a universal modulus-independent lattice when the charges are defined to be the canonical charges corresponding to the quantum supergravity symmetry groups.