Abstract
The Charge Convexity Conjecture (CCC) states that in a unitary conformal field theory in d ≥ 3 dimensions with a global symmetry, the minimal dimension of operators in certain representations of the symmetry, as a function of the charge q of the representation (or a generalized notion of it), should be convex. More precisely, this was conjectured to be true when q is restricted to positive integer multiples of some integer q0. The CCC was tested on a number of examples, most of which are in d < 4 dimensions, and its version in which q0 is taken to be the charge of the lowest-dimension positively-charged operator was shown to hold in all of them.
In this paper we test the conjecture in a non-trivial example of a d = 4 theory, which is the family of Caswell-Banks-Zaks IR fixed points of SU(Nc) gauge theory coupled to Nf massless fermions and Ns massless scalars. In these theories, the lowest-dimension gauge-invariant operators that transform non-trivially under the global symmetry are mesons. These may consist of two scalars, two fermions or one of each.
We find that the CCC holds in all applicable cases, providing significant new evidence for its validity, and suggesting a stronger version for non-simple global symmetry groups.
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Acknowledgments
We would like to thank Eran Palti, Adar Sharon, Tomer Solberg and Masataka Watanabe for useful discussions. This work was supported in part by an Israel Science Foundation (ISF) center for excellence grant (grant number 2289/18), by ISF grant no. 2159/22, by Simons Foundation grant 994296 (Simons Collaboration on Confinement and QCD Strings), by grant no. 2018068 from the United States-Israel Binational Science Foundation (BSF), by the Minerva foundation with funding from the Federal German Ministry for Education and Research, by the German Research Foundation through a German-Israeli Project Cooperation (DIP) grant “Holography and the Swampland”, and by a research grant from Martin Eisenstein. OA is the Samuel Sebba Professorial Chair of Pure and Applied Physics.
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Aharony, O., Breitstein, YN. Tests of the Charge Convexity Conjecture in Caswell-Banks-Zaks theory. J. High Energ. Phys. 2023, 44 (2023). https://doi.org/10.1007/JHEP08(2023)044
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DOI: https://doi.org/10.1007/JHEP08(2023)044