On the Green function for an Aharonov-Bohm flux tube

TL;DR

This paper explores the Green function for a scalar field around a magnetic flux tube with a conical singularity, connecting it to special functions and defect expansions in conformal field theory.

Contribution

It demonstrates how the Green function relates to special functions and defect block expansions, providing new insights into the mathematical structure of the problem.

Findings

Green function expressed as Picard integral of Appell F1

Transformation to confluent Horn function analyzed

Connections to defect block expansions in CFT established

Abstract

An earlier contour expression for the Green function of a free complex scalar field in the presence of a conical singularity with localised magnetic flux is shown to yield expressions for the field correlator and defect block expansions that have been more recently found in connection with monodromy defects in conformal field theory. The Green function appears as the Picard integral representation of the Appell $F_1$ function. This is shown to transform into a confluent Horn function, corresponding to a different defect block expansion. Other transformations are discussed.