Abstract
The Weak Gravity Conjecture is typically stated as a bound on the mass-to-charge ratio of a particle in the theory. Alternatively, it has been proposed that its natural formulation is in terms of the existence of a particle which is self-repulsive under all long-range forces. We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with non-negative self-binding energy. This formulation is particularly interesting in anti-de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let $\Delta(q)$ be the dimension of the lowest-dimension operator with charge $q$ under some global $U(1)$ symmetry, then $\Delta(q)$ must be a convex function of $q$. This formulation avoids any reference to holographic dual forces or even to locality in spacetime, and so we make a wild leap, and conjecture that such convexity of the spectrum of charges holds for any (unitary) conformal field theory, not just those that have weakly coupled and weakly curved duals. This Charge Convexity Conjecture, and its natural generalization to larger global symmetry groups, can be tested in various examples where anomalous dimensions can be computed, by perturbation theory, $1/N$ expansions and semi-classical methods. In all examples that we tested we find that the conjecture holds. We do not yet understand from the CFT point of view why this is true.
Highlights
In this paper we consider properties of local operators in unitary conformal field theories (CFTs) with continuous global symmetries
We propose a closely related, but distinct, formulation, which is that it should correspond to a particle with non-negative self-binding energy. This formulation is interesting in anti–de Sitter space, because it has a simple conformal field theory (CFT) dual formulation: let ΔðqÞ be the dimension of the lowest-dimension operator with charge q under some global Uð1Þ symmetry, ΔðqÞ must be a convex function of q
In this paper we discussed a different formulation of the weak gravity conjecture [1] (WGC) in terms of binding energy, and this has a simpler formulation in the dual CFT, as the convex charge conjecture (1.1) that we presented in the Introduction
Summary
In this paper we consider properties of local operators in unitary conformal field theories (CFTs) with continuous global symmetries (in d > 2 space-time dimensions). We propose that such operators should satisfy a certain convexitylike property: Abelian Convex Charge Conjecture: Consider any CFT with a Uð1Þ global symmetry. By a self-binding energy here we mean the difference of energies between the lowest two-particle state and twice the energy of the one-particle state This formulation is closely related to previous formulations, most closely to selfrepulsive statements [2,3], but has some important differences which become more pronounced in anti–de Sitter (AdS) space.
Sign-in/Register to view highlights & summary 
Published Version (
Free)
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call