Anomaly Holography, the Wess-Zumino-Witten Term, and Electroweak Symmetry Breaking

TL;DR

This paper explores anomalies in holographic effective field theories of gauge fields in AdS_5, deriving constraints and the form of the Wess-Zumino-Witten term, with implications for electroweak symmetry breaking models.

Contribution

It computes the WZW term in holographic EFTs and analyzes anomaly constraints, distinguishing models with and without the WZW term in electroweak symmetry breaking.

Findings

Anomalies impose stronger constraints than 4D anomaly cancellation.

The WZW term's form is explicitly computed in the holographic context.

Minimal composite Higgs models lack a WZW term, unlike some other models.

Abstract

I consider anomalies in effective field theories (EFTs) of gauge fields coupled to fermions on an interval in AdS_5, 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.