Semiclassical Canovaccio for Composite Operators

TL;DR

This paper introduces a new semiclassical approach to compute the scaling dimensions of heavy neutral composite operators in conformal field theories, expanding analytical tools for inaccessible regimes.

Contribution

It develops a semiclassical framework that maps scaling dimensions to energy spectra of classical configurations, applicable to various CFTs and demonstrated on $\

Findings

Determined the spectrum of neutral operators in $\

Applicable to $\

Provides a pedagogical presentation of the methodology.

Abstract

We present a novel semiclassical framework tailored to determine the scaling dimensions of heavy neutral composite operators in conformal field theories (CFTs) which are inaccessible with other current methodologies. It utilizes the state-operator correspondence to map the desired scaling dimensions to the semiclassical energy spectrum of periodic homogeneous field configurations on a cylinder. As concrete applications, we provide detailed analyses for the $\phi^4$ theory near four dimensions and $\phi^6$ near three dimensions, semiclassically determining the full spectrum of neutral operators in the traceless symmetric Lorentz representations. Our methodology is presented pedagogically and is readily applicable to a vast class of CFTs.