Large-N expansion, conformal field theory and renormalization-group flows in three dimensions

TL;DR

This paper investigates three-dimensional conformal field theories using large-N expansion and modified dimensional regularization, revealing dualities, exact relations, and addressing regularization issues to advance understanding of odd-dimensional CFTs.

Contribution

It introduces a novel approach combining large-N and modified regularization to study 3D conformal theories, uncovering dualities and fixing regularization problems.

Findings

Discovery of non-perturbative dualities between fixed points.

Establishment of an exact relation between beta function and anomalous dimension.

Identification and resolution of issues with naive dimensional regularization.

Abstract

I study a class of interacting conformal field theories and conformal windows in three dimensions, formulated using the Parisi large-N approach and a modified dimensional-regularization technique. Bosons are associated with composite operators and their propagators are dynamically generated by fermion bubbles. Renormalization-group flows between pairs of interacting fixed points satisfy a set of non-perturbative g <-> 1/g dualities. There is an exact relation between the beta function and the anomalous dimension of the composite boson. Non-Abelian gauge fields have a non-renormalized and quantized gauge coupling, although no Chern-Simons term is present. A problem of the naive dimensional-regularization technique for these theories is uncovered and removed with a non-local, evanescent, non-renormalized kinetic term. The models are expected to be a fruitful arena for the study of odd-dimensional conformal field theory.