Correlation functions in the Schwarzian theory

TL;DR

This paper introduces a rigorous method using quasi-invariant measures to evaluate correlation functions in the Schwarzian theory, advancing the mathematical understanding of theories with infinite-dimensional symmetries.

Contribution

It presents a novel, mathematically rigorous approach to compute correlation functions in the Schwarzian theory using measures on diffeomorphism groups.

Findings

Explicit evaluation of correlation functions in the Schwarzian theory.

Development of a mathematically correct framework for infinite-dimensional symmetry groups.

Application of the method to a key example in the Schwarzian model.

Abstract

A mathematically correct approach to study theories with infinite-dimensional groups of symmetries is presented. It is based on quasi-invariant measures on the groups. In this paper, the properties of the measure on the group of diffeomorphisms are used to evaluate the functional integrals in the Schwarzian theory. As an important example of the application of the new technique, we explicitly evaluate the correlation functions in the Schwarzian theory.