Abstract
We examine the Abelian Higgs model in (d + 1)-dimensional anti-de Sitter space with an ultraviolet brane. The gauge symmetry is broken by a bulk Higgs vacuum expectation value triggered on the brane. We propose two separate Goldstone boson equivalence theorems for the boundary and bulk degrees of freedom. We compute the holographic self-energy of the gauge field and show that its spectrum is either a continuum, gapped continuum, or a discretuum as a function of the Higgs bulk mass. When the Higgs has no bulk mass, the AdS isometries are unbroken. We find in that case that the dual CFT has a non-conserved U(1) current whose anomalous dimension is proportional to the square of the Higgs vacuum expectation value. When the Higgs background weakly breaks the AdS isometries, we present an adapted WKB method to solve the gauge field equations. We show that the U(1) current dimension runs logarithmically with the energy scale in accordance with a nearly-marginal U(1)-breaking deformation of the CFT.
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Acknowledgments
Kuntal Pal contributed to early aspects of this study. We thank Csaba Csáki, Lexi Costantino, Liam Fitzpatrick, Gero von Gersdorff, Eugenio Megias, David Meltzer, Maxim Perelstein, Mariano Quiros and Brian Shuve for insightful discussions. PT thanks the Aspen Center for Physics (NSF grant #1066293), the Kavli Institute for Theoretical Physics (NSF PHY-1748958 and PHY-2309135), the 2022 Pollica Summer Workshop on Dark Matter, the SAIFR/Principia Workshop on the Nature of Dark Matter, and the Center for Theoretical Underground Physics and Related Areas (CETUP∗) for their hospitality during a period where part of this work was completed. PT is supported by an NSF CAREER award (#2045333).
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Chaffey, I., Fichet, S. & Tanedo, P. Holography of broken U(1) symmetry. J. High Energ. Phys. 2024, 330 (2024). https://doi.org/10.1007/JHEP05(2024)330
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DOI: https://doi.org/10.1007/JHEP05(2024)330