On the bulk block expansion for a monodromy defect

TL;DR

This paper derives a formula for the finite part of correlators involving a monodromy defect in free fields, expressing it as a double power series linked to bulk block expansion, with explicit coefficients and simplified representations.

Contribution

It introduces a new explicit formula for the bulk block expansion of correlators with monodromy defects, connecting hypergeometric functions and Appell functions for simplified analysis.

Findings

Derived a double power series formula for correlators

Expressed coefficients explicitly in terms of flux and dimension

Rewrote the expansion as an Appell F3 function for simplicity

Abstract

For a free--field flat monodromy defect, a formula for the finite part of the correlator is obtained as a double power series in $(1-x)$ and $(1-\ol x)$ where $x$ and $\ol x$ are lightcone coordinates. It takes the particular form of a series in $(1-x)$ with coefficients finite sums of hypergeometric functions of $1-\ol x$ and is identified with a bulk block expansion. A simple expression for the coefficient of the $(1-x)^n(1-\ol x)^m$ term is thereby found as an explicit function of the flux and dimension. Some typical examples are presented.A transformation allows the bulk block expansion to be written as an Appell $F_3$ function which has simplifying consequences.