Effective Potential for D-brane in Constant Electromagnetic Field

TL;DR

This paper calculates the one-loop and static potentials for toroidal D-branes in constant electromagnetic fields, revealing magnetic fields can stabilize D-branes while electric fields tend to destabilize them.

Contribution

It provides explicit calculations of effective potentials for D-branes under constant electromagnetic backgrounds, highlighting the stabilizing effect of magnetic fields and the destabilizing effect of electric fields.

Findings

Magnetic background can stabilize D-branes, allowing non-pointlike ground states.

Electric background destabilizes D-branes, with the one-loop potential unbounded from below.

Static potential exhibits stable minima, detailed in the analysis.

Abstract

We discuss the one-loop effective potential and static (large $d$) potential for toroidal D-brane described by DBI-action in constant magnetic and in constant electric fields. Explicit calculation is done for membrane case ($p=2$) for both types of external fields and in case of static potential for an arbitrary $p$. In the case of one-loop potential it is found that the presence of magnetic background may stabilize D-brane giving the possibility for non-pointlike ground state configuration. On the same time, constant electrical field acts against stabilization and the correspondent one-loop potential is unbounded from below. The properties of static potential which also has stable minimum are described in detail. The back-reaction of quantum gauge fields to one-loop potential is also evaluated.