Boundary Scattering in 1+1 Dimensions as an Aharanov-Bohm Effect

TL;DR

This paper reveals that boundary scattering in 1+1 dimensional conformal field theories can be understood as an Aharonov-Bohm effect, using a topological perspective via Chern-Simons theory, providing new insights into boundary interactions.

Contribution

It introduces a topological reformulation of boundary scattering in 1+1 D CFT as an Aharonov-Bohm effect through Chern-Simons correspondence, offering a novel derivation of scalar field scattering.

Findings

Boundary scattering is equivalent to an Aharonov-Bohm effect.

Topological origin simplifies the derivation of boundary scattering.

Provides a new perspective linking CFT boundary problems to topological gauge theories.

Abstract

The boundary scattering problem in 1+1 dimensional CFT is relevant to a multitude of areas of physics, ranging from the Kondo effect in condensed matter theory to tachyon condensation in string theory. Invoking a correspondence between CFT on 1+1 dimensional manifolds with boundaries and Chern-Simons gauge theory on 2+1 dimensional Z_2 orbifolds, we show that the 1+1 dimensional conformal boundary scattering problem can be reformulated as an Aharonov-Bohm effect experienced by chiral edge states moving on a 1+1 dimensional boundary of the corresponding 2+1 dimensional Chern-Simons system. The secretly topological origin of this physics leads to a new and simple derivation of the scattering of a massless scalar field on the line interacting with a sinusoidal boundary potential.