The mass formula for a fundamental string as a BPS solution of a D-brane's worldvolume

TL;DR

This paper introduces a generalized mass formula for fundamental strings as BPS solutions on D-brane worldvolumes, validated in both flat and curved backgrounds, revealing conditions under which the energy matches the string mass.

Contribution

It proposes a new mass formula for fundamental strings as BPS solutions on D-branes, extending previous understanding to curved backgrounds and analyzing its validity.

Findings

Mass of strings proportional to geodesic distance in curved backgrounds

Agreement between string mass and D-brane energy holds only in flat backgrounds

Validation of the mass formula through point charge solutions in D-8-brane backgrounds

Abstract

We propose a (generalized) ``mass formula'' for a fundamental string described as a BPS solution of a D-brane's worldvolume. The mass formula is obtained by using the Hamiltonian density on the worldvolume, based on transformation properties required for it. Its validity is confirmed by investigating the cases of point charge solutions of D-branes in a D-8-brane (i.e. curved) background, where the mass of each of the corresponding strings is proportional to the geodesic distance from the D-brane to the point parametrized by the (regularized) value of a transverse scalar field. It is also shown that the mass of the string agrees with the energy defined on the D-brane's worldvolume only in the flat background limit, but the agreement does not always hold when the background is curved.