Localized Backreacted Flavor Branes in Holographic QCD

TL;DR

This paper studies the small backreaction effects of localized D8 branes in holographic QCD models, showing that the background remains stable and smooth within a certain perturbative regime, preserving the original embedding and meson stability.

Contribution

It provides explicit expressions for the backreacted metric, dilaton, and RR form in the D4-D8 system, demonstrating stability and smoothness under perturbative backreaction.

Findings

Backreaction remains small up to a certain radial distance.

Background functions are smooth except at D8 sources.

Scalar mesons do not become tachyonic due to backreaction.

Abstract

We investigate the perturbative (in $g_s N_{D8}$) backreaction of localized D8 branes in D4-D8 systems including in particular the Sakai Sugimoto model. We write down the explicit expressions of the backreacted metric, dilaton and RR form. We find that the backreaction remains small up to a radial value of $u \ll \ell_s/(g_s N_{D8})$, and that the background functions are smooth except at the D8 sources. In this perturbative window, the original embedding remains a solution to the equations of motion. Furthermore, the fluctuations around the original embedding, describing scalar mesons, do not become tachyonic due to the backreaction in the perturbative regime. This is is due to a cancelation between the DBI and CS parts of the D8 brane action in the perturbed background.