IR Free or Interacting? A Proposed Diagnostic

TL;DR

This paper proposes a criterion based on the conformal anomaly 'a' to determine whether a 4d quantum field theory is IR free or conformal, and tests it in supersymmetric theories with consistent results.

Contribution

It introduces a conjecture linking the IR phase of 4d theories to the conformal anomaly 'a' and verifies it across multiple supersymmetric examples.

Findings

The conjecture correctly predicts IR phases in tested cases.

It suggests the IR phase for SU(2) with isospin 3/2 is conformal.

The stronger operator-based conjecture also holds in tested scenarios.

Abstract

We present and discuss a conjectured criterion for determining whether a 4d quantum field theory is IR free, or flows to an interacting conformal field theory in the infrared: ``the correct infrared phase is that with the larger conformal anomaly $a$". A stronger conjecture is that ``an operator can become IR free only if that results in a larger conformal anomaly $a$". We test these conjectures in the context of N=1 supersymmetric theories. They are verified to indeed predict the correct IR phase in every tested case, for a plethora of examples for which the infrared phase could already be determined on other grounds. When applied to the still unsettled case of SU(2) with a chiral superfield in the isospin 3/2 representation, the conjecture suggest that the IR phase is conformal rather than confining.