Unusual view of the Schwarzian theory

TL;DR

This paper introduces a novel decomposition of the Wiener measure to facilitate the analysis of the Schwarzian theory, connecting it to a tachyonic model with Calogero potential via Fourier transform.

Contribution

It proposes a new decomposition method of the Wiener measure based on quasi-invariance, enabling a new representation of Schwarzian theory integrals.

Findings

Functional integrals in Schwarzian theory expressed as Fourier transforms.

Connection established between Schwarzian theory and tachyonic Calogero model.

New mathematical framework for analyzing Schwarzian-related models.

Abstract

A decomposition of the Wiener measure based on its quasi-invariance under the group of diffeo- morphisms is proposed. As a result, functional integrals in the Schwarzian theory can be written as the Fourier transform of the integrals in a tahyonic model with the Calogero potential.