Correlation functions in the Schwarzian theory

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.

29 pages, 3 figures

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• Simple rules of functional integration in the Schwarzian theory: SYK correlators
• Path Integrals in Quadratic Gravity
• Polar decomposition of the Wiener measure: Schwarzian theory versus conformal quantum mechanics
• Cosmology as a CFT${}_1$
• An Approach to Quantum 2D Gravity
• Functional integration over the factor-space $Dif{f}_{+}^1(S^1)/SL(2,\text{R})$