On R-symmetric Fixed Points and Superconformality

TL;DR

This paper proves that in four-dimensional quantum field theories, certain R-symmetric fixed points are necessarily superconformal, clarifying the conditions under which scale invariance implies full conformal invariance.

Contribution

It provides a non-perturbative proof that specific R-symmetric fixed points in four dimensions are superconformal, advancing understanding of conformal symmetry in quantum field theory.

Findings

R-symmetric fixed points are necessarily superconformal in 4D

Infrared fixed points of N=1 supersymmetric QCD are superconformal

Establishes a non-perturbative relation between scale and conformal invariance

Abstract

An important unanswered question in quantum field theory is to understand precisely under which conditions scale invariance implies invariance under the full conformal group. While the general answer in two dimensions has been known for over twenty years, a precise non-perturbative relation between scale and conformal invariance in higher dimensions has been lacking. In this note, we specialize to four dimensions and give a full quantum mechanical proof that certain unitary R-symmetric fixed points are necessarily superconformal. Among other consequences, this result implies that the infrared fixed points of N=1 supersymmetric quantum chromodynamics are superconformal.