Anomaly Inflow and Holography

TL;DR

This paper explores the anomaly inflow mechanism in a five-dimensional AdS spacetime with branes, providing a comprehensive holographic analysis of anomalies, symmetry breaking, and dual CFT descriptions, including new insights into anomaly matching and WZW quantization.

Contribution

It offers a unified holographic framework for anomaly inflow, dual CFT interpretation, and detailed analysis of symmetry breaking and anomaly matching in AdS/CFT correspondence.

Findings

Reproduces known anomaly matching results in holography.

Shows anomaly inflow is free of mixed anomalies with confining gauge forces.

Provides a holographic derivation of WZW quantization conditions.

Abstract

We systematically study the anomaly inflow by the bulk Chern-Simons (CS) theory in a slice of five-dimensional anti-de Sitter spacetime ($\text{AdS}_5$). The introduction of UV and IR 3-branes makes the anomaly story remarkably rich and many interesting aspects can be obtained, including weakly gauging and spontaneous symmetry breaking of the global symmetries of the dual 4D CFT. Our main contribution is to provide a unified and comprehensive discussion of the subject, together with a detailed description of the dual CFT picture for each case. Employing a gauge-fixed effective action suitable for a holographic study, we reproduce many known results in the literature, such as 't Hooft anomaly matching for unbroken symmetry (Neumann IR-BC) and (gauged) Wess-Zumino-Witten (WZW) action for broken symmetry (IR-BC breaks the bulk group $G \to H$). In addition, we show that anomaly matching occurs for ABJ anomalies as well as 't Hooft anomalies, which suggests anomalies inflowed from the bulk CS theory are necessarily free of mixed anomalies with the confining gauge force of the 4D dual CFT. In the case of broken symmetry, we prove that the "would-be" Goldstone bosons associated with the weakly gauged symmetry are completely removed by a proper field redefinition, provided the anomaly from the bulk is exactly cancelled by the boundary contribution, hence confirming the standard expectation. Moreover, we present a holographic formulation of Witten's argument for the quantization condition for the WZW action, and argue in favor of an alternative way to obtain the same condition using a "deformed" theory (different BCs). We work out several examples, including a product group with mixed anomaly, and identify the corresponding dual CFT picture. We consider a fully general case typically arising in the context of dynamical electroweak symmetry breaking.