Further on the Aharonov-Bohm Green function: the coincidence limit

TL;DR

This paper derives a subtracted Green function for scalar CFTs with monodromy defects, proving a conjecture and extending it to generalised free fields, with implications for bulk block expansions and finite limits.

Contribution

It introduces a new expression for the Green function involving Appell functions and proves a conjecture relating to monodromy defects in scalar CFTs.

Findings

Derived a subtracted Green function in terms of Appell F1 functions.

Proved and extended a conjecture by Gimenez-Grau and Liendo.

Expressed finite coincidence limits using Beta functions.

Abstract

For a scalar CFT with a monodromy defect, a `subtracted Green function' is derived in terms of an Appell $F_1$ function. A conjectured relation of Gimenez-Grau and Liendo is thereby proved and extended and shown to hold for generalised free fields. A possible means of determining the bulk block expansion is outlined. Finite coincidence limits are expressed as combinations of Beta functions.