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A counterexample to the CFT convexity conjecture
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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.
Forward citations
Cited by 3 Pith papers
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Towers of Operators in CFTs and Convexity Bounds at Large Charge
In 3d CFTs with moduli spaces, the projected large-charge tower obeys the convexity bound α0≤0, while the leading slope α1 has no universal bound besides α1≥0.
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Quantum corrections to DGKT and the Weak Gravity Conjecture
Quantum corrections from gaugino condensation and D2 instantons lift the DGKT D4-brane moduli space, making the branes self-attractive and putting the vacuum in tension with the membrane WGC.
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Relative Quantum Gravity: Localized Gravity and the Swampland
Localized gravity theories can violate swampland constraints, but satisfy them when defined relative to a higher-dimensional gravity completion, dubbed relative quantum gravity.
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