Fate of the Born-Infeld solution in string theory

TL;DR

This paper demonstrates that the classical Born-Infeld solution on D9-branes becomes unstable when derivative corrections from string theory are considered, leading to the absence of finite-energy electrostatic solutions.

Contribution

It shows that the Born-Infeld solution is unstable under string-theoretic derivative corrections, challenging its classical stability and applicability.

Findings

No finite-energy electrostatic solutions with first-order corrections

Derivative corrections destabilize classical Born-Infeld solutions

Implications for D-brane stability in string theory

Abstract

We argue that the Born-Infeld solution on the D$9-$brane is unstable under inclusion of derivative corrections to Born-Infeld theory coming from string theory. More specifically, we find no electrostatic solutions to the first order corrected Born-Infeld theory on the D$9-$brane which give a finite value for the Lagrangian.