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A<sc>bstract</sc> 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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Counting operators in N = 1 supersymmetric gauge theories
A<sc>bstract</sc> Following a recent publication, in this paper we count the number of independent operators at arbitrary mass dimension inN= 1 supersymmetric gauge theories and derive their field and derivative content. This work uses Hilbert series machinery and extends a technique from our previous work on handling integration by parts redundancies to vector superfields. The method proposed here can be applied to both abelian and non-abelian gauge theories and for any set of (chiral/antichiral) matter fields. We work through detailed steps for the abelian case with single flavor chiral superfield at mass dimension eight, and provide other examples in the appendices.
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- Award ID(s):
- 2112540
- PAR ID:
- 10546085
- Publisher / Repository:
- Journal of High Energy Physics
- Date Published:
- Journal Name:
- Journal of High Energy Physics
- Volume:
- 2023
- Issue:
- 7
- ISSN:
- 1029-8479
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/JHEP07(2023)081
