Holographic QCD Integrated back to Hidden Local Symmetry

TL;DR

This paper introduces a gauge-invariant method to integrate out infinite KK modes in holographic QCD, simplifying the model to chiral perturbation theory with hidden local symmetry, and successfully computes form factors matching experimental data.

Contribution

The paper presents a novel gauge-invariant technique to incorporate effects of infinite KK modes into low-energy effective theories of holographic QCD, specifically reducing to HLS with explicit calculations.

Findings

Computed pion electromagnetic form factors consistent with experiments.

Determined ${ m O}(p^4)$ and ${ m O}(p^2)$ terms including higher KK mode effects.

Analyzed anomaly-related vertex functions with full KK mode contributions.

Abstract

We develop a previously proposed gauge-invariant method to integrate out infinite tower of Kaluza-Klein (KK) modes of vector and axialvector mesons in a class of models of holographic QCD (HQCD). The HQCD is reduced by our method to the chiral perturbation theory with the hidden local symmetry (HLS) having only the lowest KK mode identified as the HLS gauge boson. We take the Sakai-Sugimoto model as a concrete HQCD, and completely determine the ${\cal O} (p^4)$ terms as well as the ${\cal O}(p^2)$ terms from the DBI part and the anomaly-related (intrinsic parity odd) gauge-invariant terms from the CS part. Effects of higher KK modes are fully included in these terms. To demonstrate power of our method, we compute momentum-dependences of several form factors such as the pion electromagnetic form factors, the $\pi^0$-$\gamma$ and $\omega$-$\pi^0$ transition form factors compared with experiment, which was not achieved before due to complication to handle infinite sums. We also study other anomaly-related quantities like $\gamma^*$-$\pi^0$-$\pi^+$-$\pi^-$ and $\omega$-$\pi^0$-$\pi^+$-$\pi^-$ vertex functions.