Bulk-boundary correspondence between charged, anyonic strings and vortices

TL;DR

This paper explores the relationship between charged, anyonic vortices in 2+1 dimensions and string-like vortices in higher dimensions, revealing a boundary-bulk correspondence that links their fractional statistics and implications for dualities like AdS/CFT.

Contribution

It introduces a unified framework connecting boundary vortices and bulk strings, demonstrating how their fractional statistics are related and can be derived from boundary measurements.

Findings

Boundary phase shifts match between bulk strings and boundary vortices.

Fractional statistics arise from Aharonov-Bohm effects in both cases.

The framework applies to theories with topological terms and external currents.

Abstract

We discuss a unified framework of dealing with electrically charged, anyonic vortices in 2+1 dimensional spacetimes and extended, anyonic string-like vortices in one higher dimension. We elaborate on two ways of charging these topological objects and point out that in both cases the vortices and strings obey fractional statistics as a consequence of being electrically charged. The statistics of the charged vortices and strings can be obtained from the phase shift of their respective wave-functions under the classic Aharonov-Bohm type experiments. We show that for a manifold with boundary, where one can realize 2+1 dimensional vortices as endpoints of trivially extended 3+1 dimensional strings, there is a smooth limit where the phase shift of a bulk string-vortex goes over to the phase shift of the boundary vortex. This also enables one to read off the bulk statistics (arising essentially from either a QCD theta-type term or an external current along the string) just from the corresponding boundary statistics in a generic setting. Finally, we discuss various applications of these findings, and in particular their prospects for the AdS/CFT duality.