A counterexample to the CFT convexity conjecture

Abstract

Motivated by the weak gravity conjecture, arXiv:2108.04594 conjectured that in any CFT, the minimal operator dimension at fixed charge is a convex function of the charge. In this letter we construct a counterexample to this convexity conjecture, which is a clockwork-like model with some modifications to make it a weakly-coupled CFT. We also discuss further possible applications of this model and some modified versions of the conjecture which are not ruled out by the counterexample.

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Cited by in corpus (2)

• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• Tests of the Charge Convexity Conjecture in Caswell-Banks-Zaks Theory