Abstract
I consider anomalies in effective field theories (EFTs) of gauge fields coupled to fermions on an interval in AdS5, and their holographic duals. The anomalies give rise to constraints on the consistent EFT description, which are stronger than the usual four-dimensional anomaly cancellation condition for the zero modes. Even though the anomalies occur on both boundaries of the interval, corresponding to both the UV and the IR of the holographic dual, they are nevertheless consistent with the non-renormalization of the anomaly and the 't Hooft matching condition. They give rise, in general, to a Wess–Zumino–Witten (WZW) term in the four-dimensional, low-energy effective action, whose form I compute. Finally I discuss the relevance to holographic models of electroweak symmetry breaking. I show that the so-called ‘minimal composite Higgs models’ have a consistent EFT description without a WZW term. In contrast, a variant of an earlier model of Contino, Nomura, and Pomarol does have a WZW term.
Highlights
The AdS/CFT [1] correspondence has given rise to new solutions to the hierarchy problem of electroweak symmetry breaking (EWSB) [2]. In their most sophisticated form [3, 4], these consist of gauge theories coupled to fermions on an interval of an AdS5 geometry, with the scalar Higgs sector of the Standard Model arising from the fifth-dimensional components of the gauge fields
Gauge theories of this type, living on an interval in d = 5, suffer from anomalies. These anomalies, which are localized on the four-dimensional boundaries of the interval, arise variously from fermions and from bulk Chern-Simons (CS) terms for the gauge fields. This has been known for some time [8, 9], but appears to have been disregarded in the literature on holographic models of EWSB, perhaps with the tacit assumption that, provided the usual d = 4 anomaly cancellation condition is satisfed for the gauge and fermion zero modes, the fermionic boundary anomalies can always be cancelled by suitable CS terms
In the usual formulation of a gauge theory on an interval, the bulk G gauge invariance is allowed to be broken to subgroups H0,1 on the boundaries, by choosing the Dirichlet boundary conditions (BCs) for the fifth components, A5, of gauge fields corresponding to generators in Lie(H0) on the UV boundary, and the Neumann BC for the others
Summary
The AdS/CFT [1] correspondence has given rise to new solutions to the hierarchy problem of electroweak symmetry breaking (EWSB) [2]. Even if the anomalies can be cancelled, there will still, in general, be observable physics associated with the anomaly, that one might hope to explore at upcoming collider experiments This physics takes the form of Wess-Zumino-Witten (WZW) terms [15, 16] in the low-energy effective action, that reproduce the UV anomalies of non-linearly realized symmetries, in accordance with ’t Hooft’s condition [17]. This is analogous to what happens in the strong interaction. We have all the necessary ingredients to built a locally G-invariant, G/H-coset sigma model, coupled to matter transforming in representations of either H or G
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