Towards bosonization of Virasoro coadjoint orbits

TL;DR

This paper demonstrates that Schwarzian theories linked to specific Virasoro coadjoint orbits can be bosonized, enabling explicit computation of correlation functions through a Gaussian path integral in a special Darboux chart.

Contribution

It introduces a bosonization approach for Schwarzian theories on certain Virasoro coadjoint orbits, providing a new geometric framework for analysis.

Findings

Existence of a global $S^1$-equivariant Darboux chart for hyperbolic and parabolic orbits

Explicit computation of bilocal correlation functions in this chart

Conjecture of similar structure for the Teichmüller orbit

Abstract

We show that Schwarzian theories associated to certain hyperbolic and parabolic Virasoro coadjoint orbits admit bosonization, i.e. a global $S^1$-equivariant Darboux chart in which the corresponding path integral becomes Gaussian. In this chart, correlation functions of bilocals, time-ordered and out-of-time ordered, can be computed explicitly. We conjecture that a similar global chart exists for the Teichm\"uller orbit.