BPS Mass, Dirichlet Boundary Condition, and the Isotropic Coordinate System

TL;DR

This paper investigates BPS bounds and boundary conditions for strings and branes in specific backgrounds, highlighting the role of isotropic coordinates and the dynamic emergence of Dirichlet boundary conditions.

Contribution

It introduces a novel perspective on BPS bounds using isotropic coordinates and demonstrates how Dirichlet boundary conditions are dynamically induced in these systems.

Findings

BPS bounds are measured by isotropic coordinates rather than spacetime geometry.

Ground state energy is independent of gravitational radii.

Dirichlet boundary conditions are dynamically induced in perturbations.

Abstract

We consider test strings and test branes ending on D$p$-branes ($p\le 6$) and NS5-branes in the background, for a heuristic understanding of the dynamics. Whenever some supersymmetry is preserved, a simple BPS bound appears, but the central charge in question is measured by certain isotropic coordinate system, rather than by the actual spacetime geometry. This way, the ground state energy is independent of the gravitational radii of the solitonic background. Furthermore, a perturbation around the supersymmetric ground states reveals that the appropriate Dirichlet boundary condition is dynamically induced. We close with comments.