Local recoil of extended solitons: a string theory example

TL;DR

This paper explores the phenomenon of local recoil in extended solitons, particularly vortex lines, highlighting its geometric nature, connection to infrared divergences, and how string theory techniques can resolve these divergences to produce finite scattering amplitudes.

Contribution

It demonstrates the geometric manifestation of local recoil in vortex lines and shows how string theory methods can resum divergences to obtain finite results.

Findings

Recoil causes finite displacements proportional to transferred momentum.

Infrared divergences in perturbation theory are associated with local recoil.

Resummation techniques yield finite, momentum-conserving scattering amplitudes.

Abstract

It is well-known that localized topological defects (solitons) experience recoil when they suffer an impact by incident particles. Higher-dimensional topological defects develop distinctive wave patterns propagating along their worldvolume under similar circumstances. For 1-dimensional topological defects (vortex lines), these wave patterns fail to decay in the asymptotic future: the propagating wave eventually displaces the vortex line a finite distance away from its original position (the distance is proportional to the transferred momentum). The quantum version of this phenomenon, which we call ``local recoil'', can be seen as a simple geometric manifestation of the absence of spontaneous symmetry breaking in 1+1 dimensions. Analogously to soliton recoil, local recoil of vortex lines is associated with infrared divergences in perturbative expansions. In perturbative string theory, such divergences appear in amplitudes for closed strings scattering off a static D1-brane. Through a Dirac-Born-Infeld analysis, it is possible to resum these divergences in a way that yields finite, momentum-conserving amplitudes.