Potentials between D-Branes in a Supersymmetric Model of Space-Time Foam

TL;DR

This paper models space-time foam using supersymmetric D-branes and D-particles, calculating vacuum energy contributions from their interactions, which may relate to cosmological phenomena like inflation and Dark Energy.

Contribution

It introduces a detailed calculation of vacuum energy in a supersymmetric D-brane system with moving branes and D-particles, linking string interactions to cosmological implications.

Findings

Vacuum energy depends on brane and D-particle velocities and separations.

Interactions lead to a positive, non-trivial vacuum energy.

Framework for brane inflation and residual Dark Energy in cosmology.

Abstract

We study a supersymmetric model of space-time foam with two stacks each of eight D8-branes with equal string tensions, separated by a single bulk dimension containing D0-brane particles that represent quantum fluctuations. The ground-state configuration with static D-branes has zero vacuum energy, but, when they move, the interactions among the D-branes and D-particles due to the exchanges of strings result in a non-trivial, positive vacuum energy. We calculate its explicit form in the limits of small velocities and large or small separations between the D-branes and/or the D-particles. This non-trivial vacuum energy appears as a central charge deficit in the non-critical stringy $\sigma$ model describing perturbative string excitations on a moving D-brane. These calculations enable us to characterise the ground state of the D-brane/D-particle system, and provide a framework for discussing brany inflation and the possibility of residual Dark Energy in the present-day Universe.