IR Free or Interacting? A Proposed Diagnostic

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.

17 pages. v2: added reference

References in corpus (5)

• Chiral phase structure of QCD with many flavors
• New Results on the "$a$-theorem" in Four Dimensional Supersymmetric Field Theory
• N=1 RG Flows, Product Groups, and a-Maximization
• Phase Transition Critical Flavor Number of QCD
• Higgsing and Superpotential Deformations of ADE Superconformal Theories

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