Odd Dimensional Nonlocal Liouville Conformal Field Theories

TL;DR

This paper constructs and analyzes nonlocal, non-unitary Liouville conformal field theories in odd dimensions, exploring their classical and quantum properties, including partition functions, anomalies, and correlation functions.

Contribution

It introduces a novel class of odd-dimensional Liouville CFTs with explicit formulas for their correlation functions and semi-classical approximations, extending the theory beyond even dimensions.

Findings

Derived the odd-dimensional DOZZ formula and its semi-classical limit.

Analyzed the sphere partition function and boundary conformal anomaly.

Explored correlation functions of vertex operators.

Abstract

We construct Euclidean Liouville conformal field theories in odd number of dimensions. The theories are nonlocal and non-unitary with a log-correlated Liouville field, a ${\cal Q}$-curvature background, and an exponential Liouville-type potential. We study the classical and quantum properties of these theories including the finite entanglement entropy part of the sphere partition function $F$, the boundary conformal anomaly and vertex operators' correlation functions. We derive the analogue of the even-dimensional DOZZ formula and its semi-classical approximation.