Deformation Constraints on Solitons and D-branes

TL;DR

This paper develops deformation constraints that unify and extend existing soliton stability theorems, applying them to D-branes and gravitational systems, revealing new insights into their configurations and stability conditions.

Contribution

It introduces a comprehensive set of deformation constraints that generalize Derrick's and Manton's theorems, and applies them to D-branes and gravitational systems for the first time.

Findings

Known soliton solutions satisfy the deformation constraints

New relations between soliton stability and gravitational Hamiltonian constraints

Application of constraints to D-branes with gauge fields

Abstract

We derive a set of constraints on soliton solutions using geometric deformations, and transformations by internal symmetries with space-dependent parameters. We show that Derrick's theorem and a more complete set of constraints due to Manton are special cases of these deformation constraints (DC). We demonstrate also that known soliton solutions obey the DC, and extract novel results by applying the constraints to systems of D-branes, taking into account both Dirac-Born-Infeld and Wess-Zumino actions, and examining cases with and without D-brane gauge fields. We also determine a relation with the Hamiltonian constraint for gravitational systems, and discuss configurations of finite extent, like Wilson lines.