Abstract
We use holography to study the large spin J limit of the spectrum of low energy states with charge Q under a U(1) conserved current in CFTs in d > 2 dimensions, with a focus on d = 3 and d = 4. For Q = 2, the spectrum of such states is known to be universal and properly captured by the long-distance limit of holographic theories, regardless of whether the CFT itself is holographic. We study in detail the holographic description of such states at Q > 2, by considering the contribution to the energies of Q scalar particles coming from single photon and graviton exchange in the bulk of AdS; in some cases, scalar exchange and bulk contact terms are also included. For a range of finite values of Q and J, we numerically diagonalize the Hamiltonian for such states and examine the resulting spectrum and wavefunctions as a function of the dimension ∆ of the charge-one operator and the central charges \( {c}_{\mathcal{T}} \), \( {c}_{\mathcal{J}} \) of the stress tensor and U(1) current, finding multiple regions in parameter space with qualitatively different behavior. We discuss the extension of these results to the regime of parametrically large charge Q, as well as to what extent such results are expected to hold universally, beyond the limit of holographic CFTs. We compare our holographic computations to results from the conformal bootstrap for the 3d O(2) model at Q = 3 and Q = 4 and find excellent agreement.
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Acknowledgments
We are grateful to Gabriel Cuomo, Ami Katz, Lorenzo Quintavalle, David Simmons-Duffin, and Ning Su for useful discussions, and we thank Gabriel Cuomo, Ami Katz, Petr Kravchuk, Jeremy Mann, and Lorenzo Quintavalle for comments on a draft. We especially thank David Simmons-Duffin for generously sharing some unpublished data for the O(2) model. GF, ALF, and WL are supported by the US Department of Energy Office of Science under Award Number DE-SC0015845, and GF was partially supported by the Simons Collaboration on the Non-perturbative Bootstrap.
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Fardelli, G., Fitzpatrick, A.L. & Li, W. Holography and Regge phases with U(1) charge. J. High Energ. Phys. 2024, 202 (2024). https://doi.org/10.1007/JHEP08(2024)202
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DOI: https://doi.org/10.1007/JHEP08(2024)202