Nonlocal Conformal Field Theory

TL;DR

This paper investigates nonlocal conformal field theories using fractional Virasoro algebra, revealing how nonlocal quantum dynamics relate to operator product expansions and identifying conditions for specific fixed points.

Contribution

It introduces the fractional Virasoro algebra framework to analyze nonlocal CFTs and distinguishes between Gaussian and non-Gaussian fixed points in this context.

Findings

Nonlocal quantum dynamics realize fractional Virasoro algebra with state-dependent central charge.

Gaussian fixed points with fractional Laplacian do not fit the fractional Virasoro algebra criterion.

Non-Gaussian fixed points are compatible with the fractional Virasoro algebra framework.

Abstract

Using the recently developed notion of a fractional Virasoro algebra, we explore the implied operator product expansions in nonlocal conformal field theories and their geometric meaning. We probe the interplay between classical nonlocality in the functional-analytic sense and quantization in a two-dimensional setting and find that nonlocal quantum dynamics realize this fractional Virasoro algebra exclusively with a state dependent central charge. Notably, we prove that the widely studied free Gaussian fixed points with a fractional Laplacian kinetic term does not fit this criterion but that the RG flow associated non-Gaussian fixed points do.