The structure of the spectrum of anomalous dimensions in the N-vector model in 4-epsilon dimensions

TL;DR

This paper extends previous work on the N-vector model in 4-epsilon dimensions by explicitly deriving parts of the one-loop spectrum of anomalous dimensions using conformal symmetry representations.

Contribution

It provides explicit derivations of the one-loop anomalous dimension spectrum and explores the complex structure of these spectra beyond bounds established earlier.

Findings

Explicit one-loop spectrum derived

Spectrum structure is complex and differs from 2D CFTs

Bounds on anomalous dimensions confirmed

Abstract

In a recent publication we have investigated the spectrum of anomalous dimensions for arbitrary composite operators in the critical N-vector model in 4-epsilon dimensions. We could establish properties like upper and lower bounds for the anomalous dimensions in one-loop order. In this paper we extend these results and explicitly derive parts of the one-loop spectrum of anomalous dimensions. This analysis becomes possible by an explicit representation of the conformal symmetry group on the operator algebra. Still the structure of the spectrum of anomalous dimensions is quite complicated and does generally not resemble the algebraic structures familiar from two dimensional conformal field theories.