Local recoil of extended solitons: a string theory example

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.