The Spacetime Life of a Non-BPS D-particle

TL;DR

This paper studies the classical geometry of a stable non-BPS D-particle in type IIB orbifold theory, analyzing scattering amplitudes and deriving the classical solution, revealing no-force conditions at the critical radius.

Contribution

It provides a detailed analysis of the boundary state and classical geometry of non-BPS D-particles, including force conditions and behavior at critical radius, extending understanding of non-BPS brane dynamics.

Findings

No force at order v^2 at short distances for any radius.

BPS-like behavior at the critical radius up to v^4 corrections.

Classical solutions consistent with no-force conditions at the critical radius.

Abstract

We investigate the classical geometry generated by a stable non-BPS D-particle. We consider the boundary state of a stable non-BPS D-particle in the covariant formalism in the type IIB theory orbifolded by (-1)^{F_L} I_4. We calculate the scattering amplitude between two D-particles in the non-compact and compact orbifold and analyse the short and long distance behaviour. At short distances we find no force at order $v^2$ for any radius, and at the critical radius we find a BPS-like behaviour up to $v^4$ corrections for long and short distances. Projecting the boundary state on the massless states of the orbifold closed string spectrum we obtain the large distance behaviour of the classical solution describing this non-BPS D-particle in the non-compact and compact cases. By using the non-BPS D-particle as a probe of the background geometry of another non-BPS D-particle, we recover the no-force condition at the critical radius and the $v^2$ behaviour of the probe. Moreover, assuming that the no-force persists for the complete geometry we derive part of the classical solution for the non-BPS D-particle.