A Lower-Dimensional Remnant of Flux Attachment

TL;DR

This paper explores how flux attachment phenomena, linked to Chern-Simons theory and the Aharonov-Bohm effect, can be reduced to lower dimensions, revealing a simplified remnant of the original mechanism.

Contribution

It demonstrates a dimensional reduction of flux attachment, connecting higher-dimensional Chern-Simons theory to a lower-dimensional remnant with matter coupling.

Findings

Remnant of flux attachment exists after dimensional reduction.

Connection between Chern-Simons theory and lower-dimensional phenomena.

Insights into charge-flux transmutation in reduced dimensions.

Abstract

Flux attachment is a mechanism allowing electric charges to capture magnetic flux in two spatial dimensions. Fundamentally, this is a consequence of the Aharonov-Bohm effect or, in field-theoretic language, of a Chern-Simons term. This is also intimately related to a transmutation of the exchange statistics of the original charges. We show that a remnant of this mechanism is found after a dimensional reduction of a pure Chern-Simons theory and its subsequent coupling to matter.