Extended Charged Events and Chern-Simons Couplings

TL;DR

This paper explores how Chern-Simons couplings influence extended magnetic events, leading to observable emitted objects, charge quantization conditions, and implications for higher-dimensional theories like M-theory.

Contribution

It introduces a complete action principle for extended charged events with Chern-Simons couplings, revealing new observable effects and quantization conditions, especially in higher-dimensional spacetimes.

Findings

Magnetically charged extended events emit observable extended objects.

A quantization condition for the Chern-Simons coupling is derived.

Results align with previous findings in M-theory for D=11, p=3.

Abstract

Recently, the concept of dynamical extended charged events has been introduced, and it has been argued that they should play as central a role as that played by particles or ordinary branes. In this article we show that in the presence of a Chern-Simons coupling, a magnetically charged extended event emits an extended object, which geometrically is just like a Dirac string, but it is observable, obeys equations of motion, and may be electrically charged. We write a complete action principle which accounts for this effect. The action involves two Chern-Simons terms, one integrated over spacetime and the other integrated over the worldvolume of the submanifold that is the union of the Dirac world-sheet and the history of the emitted physical object. By demanding that the total charge emitted by a composite extended magnetic event be quantized according to Dirac's rule, we find a quantization condition for the Chern-Simons coupling. For a 1-form electric potential in D=2n+1 spacetime dimensions, the composite event is formed by n elementary extended magnetic events separated in time such that the product of their transverse spaces, together with the time axis, is the entire spacetime. We show that the emitted electric charge is given by the integral of the (n-1)-th exterior power of the electromagnetic field strength over the last elementary event, or, equivalently, over an appropriate closed surface. The extension to more general p-form potentials and higher dimensions is also discussed. For the case D=11, p=3, our result for the quantization of the Chern-Simons coupling was obtained previously in the context of M-theory, a remarkable agreement that makes the existence of events even more compelling.