TY - JOUR

T1 - Convexity of charged operators in CFTs and the weak gravity conjecture

AU - Aharony, Ofer

AU - Palti, Eran

N1 - Publisher Copyright:
© 2021 authors. Published by the American Physical Society.

PY - 2021/12/15

Y1 - 2021/12/15

N2 - 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 Δ(q) be the dimension of the lowest-dimension operator with charge q under some global U(1) symmetry, then Δ(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 semiclassical 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.

AB - 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 Δ(q) be the dimension of the lowest-dimension operator with charge q under some global U(1) symmetry, then Δ(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 semiclassical 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.

UR - http://www.scopus.com/inward/record.url?scp=85120804671&partnerID=8YFLogxK

U2 - 10.1103/PhysRevD.104.126005

DO - 10.1103/PhysRevD.104.126005

M3 - Article

AN - SCOPUS:85120804671

SN - 2470-0010

VL - 104

JO - Physical Review D

JF - Physical Review D

IS - 12

M1 - 126005

ER -