Branes as BIons

TL;DR

This paper demonstrates how extreme p-brane spacetimes can be mapped to BIonic solutions with distributional sources, showing that BPS p-brane tension remains classically unrenormalized across various spacetime singularity conditions.

Contribution

It introduces a method to relate non-trivial p-brane spacetimes to BIonic solutions in a trivial topology, revealing classical unrenormalization of BPS p-brane tension.

Findings

Mapping of p-brane exteriors to BIonic solutions via harmonic coordinates

Classical unrenormalization of BPS p-brane tension

Applicability to both singular and non-singular spacetimes

Abstract

A BIon may be defined as a finite energy solution of a non-linear field theory with distributional sources. By contrast a soliton is usually defined to have no sources. I show how harmonic coordinates map the exteriors of the topologically and causally non-trivial spacetimes of extreme p-branes to BIonic solutions of the Einstein equations in a topologically trivial spacetime in which the combined gravitational and matter energy momentum is located on distributional sources. As a consequence the tension of BPS p-branes is classically unrenormalized. The result holds equally for spacetimes with singularities and for those, like the M-5-brane, which are everywhere singularity free.