A counterexample to the CFT convexity conjecture
High Energy Physics - Theory
2023-06-14 v3
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.
Cite
@article{arxiv.2301.08262,
title = {A counterexample to the CFT convexity conjecture},
author = {Adar Sharon and Masataka Watanabe},
journal= {arXiv preprint arXiv:2301.08262},
year = {2023}
}