Integrating out Holographic QCD back to Hidden Local Symmetry

TL;DR

This paper presents a gauge-invariant method to reduce holographic QCD models to hidden local symmetry chiral perturbation theory by integrating out infinite meson towers, explicitly including higher KK mode effects.

Contribution

It introduces a novel gauge-invariant technique to derive HLS-ChPT from HQCD, capturing effects of infinite KK modes in the effective theory.

Findings

Successfully reduces HQCD to HLS-ChPT with only lowest KK mode

Determines ${ m O}(p^4)$) terms fully from integrated KK modes

Demonstrates method with Sakai-Sugimoto model

Abstract

We develop a previously proposed gauge-invariant method to integrate out infinite towers of vector and axialvector mesons arising as Kaluza-Klein (KK) modes in a class of holographic models of QCD (HQCD). We demonstrate that HQCD can be reduced to the chiral perturbation theory (ChPT) with the hidden local symmetry (HLS) (so-called HLS-ChPT) having only the lowest KK mode identified as the HLS gauge boson, and the Nambu-Goldstone bosons. The ${\cal O} (p^4)$ terms in the HLS-ChPT are completely determined by integrating out infinite towers of vector/axialvector mesons in HQCD: Effects of higher KK modes are fully included in the coefficients. As an example, we apply our method to the Sakai-Sugimoto model.