A counterexample to the a-'theorem'

TL;DR

This paper discusses a counterexample to the a-theorem in four-dimensional gauge theories, clarifying previous misconceptions and emphasizing the importance of correctly understanding the low-energy limit structure.

Contribution

It corrects earlier assumptions about the low-energy limit of certain gauge theories, demonstrating that the a-theorem remains valid when multiple decoupled parts are considered.

Findings

Previous counterexamples were based on incorrect assumptions.

The low-energy limit involves multiple decoupled sectors, not a single SCFT.

The a-theorem holds when the correct low-energy structure is analyzed.

Abstract

The conclusion of the original paper was wrong, due to the incorrect assumption that the low-energy limit at the strongly-coupled point consists of a single, coupled SCFT. By taking into account the fact that the low-energy limit consists of multiple decoupled parts, it was later shown in arXiv:1011.4568 that there is no violation of the a-theorem in this system. Furthermore, the a-theorem itself was convincingly demonstrated in arXiv:1107.3987, and the argument presented there has been further refined. The rest of this paper is kept as it was, for some parts of the discussions might still be of interest. Original abstract: We exhibit a renormalization group flow for a four-dimensional gauge theory along which the conformal central charge 'a' increases. The flow connects the maximally superconformal point of an N=2 gauge theory with gauge group SU(N+1) and N_f=2N flavors in the ultraviolet, to a strongly-coupled superconformal point of the SU(N) gauge theory with N_f=2N massless flavors in the infrared. Our example does not contradict the proof of the a-theorem via a-maximization, due to the presence of accidental symmetries in the infrared limit. Nor does it contradict the holographic a-theorem, because these gauge theories do not possess weakly-curved holographic duals.