Linearized self-forces for branes

TL;DR

This paper calculates the regularized self-forces acting on branes of arbitrary dimension due to various fields, revealing how regularization affects brane tension and conditions for force cancellation.

Contribution

It introduces a method to compute and regularize self-forces on branes of any dimension in any spacetime, including gravitational and field interactions, and demonstrates tension renormalization.

Findings

Regularization leads to tension renormalization for Nambu-Goto branes.

Certain couplings can cancel the self-force on branes.

The method applies to arbitrary brane and spacetime dimensions.

Abstract

We compute the regularized force density and renormalized action due to fields of external origin coupled to a brane of arbitrary dimension in a spacetime of any dimension. Specifically, we consider forces generated by gravitational, dilatonic and generalized antisymmetric form-fields. The force density is regularized using a recently developed gradient operator. For the case of a Nambu--Goto brane, we show that the regularization leads to a renormalization of the tension, which is seen to be the same in both approaches. We discuss the specific couplings which lead to cancellation of the self-force in this case.