Holographic Non-Abelian Flavour Symmetry Breaking

TL;DR

This paper develops a holographic model to study both spontaneous and explicit non-abelian flavour symmetry breaking, incorporating running anomalous dimensions and providing numerical techniques for analyzing coupled fields.

Contribution

It introduces a bottom-up holographic framework with a bulk Higgs mechanism and a numerical method for mass eigenvalues, applied to QCD and composite Higgs scenarios.

Findings

Successfully models quark mass splitting and symmetry breaking patterns.

Provides a numerical approach tested on supersymmetric matter.

Analyzes symmetry breaking in multi-flavour QCD and exotic patterns.

Abstract

We investigate a holographic model for both spontaneous and explicit symmetry breaking of non-abelian flavour symmetries. This consists of a bottom-up model inspired by the top-down D3/D7 probe brane model that incorporates the running anomalous dimensions of the fields. We ensure that in the holographic bulk, the full non-abelian flavour symmetries for massless quarks are present. The quark masses are spontaneously generated field values in the bulk and there is a resultant bulk Higgs mechanism. We provide a numerical technique to find the mass eigenvalues for a system of coupled holographic fields. We test this approach using an analytic model of ${\cal N}=2$ supersymmetric matter. We apply this approach to two-flavour QCD with both $u-d$ quark mass splitting and multi-trace bulk action terms that are expected to break $U(N_f)_V$ to $SU(N_f)_V \times U(1)_V$ away from large $N_c$. We also discuss three-flavour QCD with strange quark mass splitting and applications to more exotic symmetry breaking patterns of potential relevance for composite Higgs models.