Janus correlators and Heun's equation

TL;DR

This paper computes two-point correlation functions for a scalar field in a Janus background, relating the equations to Heun's equation and deriving corrections to operator spectra and OPE coefficients.

Contribution

It introduces a method to relate scalar equations in Janus backgrounds to Heun's equation and calculates second-order corrections to boundary operator spectra.

Findings

Derived explicit two-point functions in Janus backgrounds.

Calculated second-order corrections to operator spectra.

Connected scalar equations to Heun's equation using connection coefficients.

Abstract

In this paper we calculate two-point correlation functions of a massive probe scalar field in the background of the three-dimensional Janus solution. We relate the equation of motion of the scalar to Heun's equation and use the recently obtained expressions for the connection coefficients to obtain the two-point function of operators dual to the probe scalar. From the correlators we obtain the corrections to the spectrum of boundary operators and bulk-boundary operator product coefficients to second order in the Janus deformation parameter.