The Decay of Unstable Noncommutative Solitons

TL;DR

This paper investigates the classical decay process of unstable scalar solitons in noncommutative field theory, revealing how decay rates depend on the noncommutativity parameter and drawing parallels to discrete breather phenomena.

Contribution

It provides a first-order calculation of decay rates of noncommutative solitons using Fermi's Golden Rule and models the decay as a nonlinear oscillator coupled to a continuum.

Findings

Decay rate computed to first order in noncommutativity parameter

Decay channel described as a nonlinear oscillator weakly coupled to linear modes

No decay occurs in the infinite noncommutativity limit

Abstract

We study the classical decay of unstable scalar solitons in noncommutative field theory in 2+1 dimensions. This can, but does not have to, be viewed as a toy model for the decay of D-branes in string theory. In the limit that the noncommutativity parameter \theta is infinite, the gradient term is absent, there are no propagating modes and the soliton does not decay at all. If \theta is large, but finite, the rotationally symmetric decay channel can be described as a highly excited nonlinear oscillator weakly coupled to a continuum of linear modes. This system is closely akin to those studied in the context of discrete breathers. We here diagonalize the linear problem and compute the decay rate to first order using a version of Fermi's Golden Rule, leaving a more rigorous treatment for future work.