Travelling Front of a Decaying Brane in String Field Theory

TL;DR

This paper models the inhomogeneous decay of an unstable D-brane in string theory using a generalized reaction-diffusion equation, analyzing its dynamics and computing related string operator functions.

Contribution

It introduces a Fisher deformation as a marginal operator in string field theory and demonstrates its consistency with the equations of motion at second order.

Findings

The decay process is described by a nonlocal, delayed reaction-diffusion equation.

The Fisher deformation satisfies the string field theory equations at second order.

One-point functions of closed string operators are computed in this setup.

Abstract

We consider the inhomogeneous decay of an unstable D-brane of bosonic string theory in a linear dilaton background in a light-cone frame. At the lowest level, the dynamical equation that describes this process is a generalisation (that includes nonlocality and time delay) of a reaction-diffusion equation studied by Fisher (and others). We argue that the equation of motion of the cubic open string field theory is satisfied at least to the second order when we start with this `Fisher deformation', a marginal operator which has a simple pole term in its OPE. We also compute the one-point functions of closed string operators on the disc in the presence of this deformation.