Correlation Function Of Thin-Shell Operators

TL;DR

This paper analyzes the correlation functions of thin-shell operators using the monodromy method, deriving solutions in specific limits, comparing with gravity, and exploring unphysical solutions and their duals.

Contribution

It introduces a novel application of the monodromy method to thin-shell operators without the probe limit and establishes a connection with gravitational calculations.

Findings

Successful computation of the Virasoro vacuum block contribution.

Perturbative solutions in probe, heavy-shell, and early-time limits.

Exact agreement between field theory and gravity results.

Abstract

In this study, we explore the correlation functions of thin-shell operators, represented semiclassically by a homogeneous, thin interface of dust particles. Employing the monodromy method, we successfully compute the contribution from the Virasoro vacuum block and present the monodromy equation in a closed form without assuming the probe limit. Although an analytical solution to the monodromy equation remains difficult, we demonstrate that it is perturbatively solvable within specific limits, including the probe, the heavy-shell, and the early-time limits. Moreover, we compare our results with gravitational calculations and find precise agreement. We strengthen our findings by proving that the thermal correlation functions in gravity, after an inverse Laplace transformation, satisfy the field theory's monodromy equation. Additionally, we identify an infinite series of unphysical solutions to the monodromy equation and discuss their potential geometrical duals.