Goldstone Bosons, Semiclassics and Convexity (Kyoto)

Abstract

The Charge Convexity Conjecture (i.e. the conjecture that the spectrum of the lowest charged operator in a CFT is a convex function of Q) implies, through holographic duality, the Positive Binding Conjecture: that gravitational theories in AdS with a U(1) gauge symmetry must contain a charged particle which has positive self-binding energy. Here we study the spectrum of scalar charged operators in CFTs with a U(1) global symmetry. We show that this spectrum is necessarily convex if it is well approximated by a field which realises the global symmetry non-linearly.