Probabilistic Correlation Functions of the Schwarzian Field Theory

TL;DR

This paper computes and characterizes correlation functions in the probabilistic Schwarzian Field Theory, confirming theoretical predictions and establishing their uniqueness, with applications to stress-energy tensor correlations.

Contribution

It provides exact calculations of correlation functions for non-intersecting Wilson lines and proves their uniqueness in characterizing the measure.

Findings

Correlation functions match predictions from conformal bootstrap and DOZZ formula.

Correlation functions uniquely determine the measure of the theory.

Stress-energy tensor correlations agree with previous formal results.

Abstract

We study correlation functions of the probabilistic Schwarzian Field Theory. We compute cross-ratio correlation functions exactly in the case when the corresponding Wilson lines do not intersect, confirming predictions made in the physics literature via limit of the conformal bootstrap and the DOZZ formula. Moreover, we prove that these correlation functions characterise the measure uniquely. We use them to define and compute the stress-energy tensor correlation functions, and demonstrate, in particular, that these agree with the results obtained earlier by formal differentiation of the partition function.