TY - JOUR

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

AU - Aharony, Ofer

AU - Palti, Eran

N1 - Funding Information:
We thank N. Arkani-Hamed, S. Chester, G. Cuomo, J. Gracey, B. Heidenreich, S. Hellerman, I. Jack, Z. Komargodski, A. Kovner, D. Kutasov, M. Lublinsky, J. Penedones, T. Rudelius, T. Ryttov, and M. Watanabe for useful discussions. The work of O. A. was supported in part by an Israel Science Foundation center for excellence grant (Grant No. 2289/18), by Grant No. 2018068 from the United States-Israel Binational Science Foundation (BSF), and by the Minerva foundation with funding from the Federal German Ministry for Education and Research. The work of E. P. was supported by the Israel Science Foundation (Grant No. 741/20). O. A. is the Samuel Sebba Professorial Chair of Pure and Applied Physics.
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

VL - 104

JO - Physical Review D - Particles, Fields, Gravitation and Cosmology

JF - Physical Review D - Particles, Fields, Gravitation and Cosmology

SN - 1550-7998

IS - 12

M1 - 126005

ER -