Subtleties of non-Abelian D-brane actions and their effect on holographic heavy-light meson spectra

TL;DR

This paper refines the holographic modeling of heavy-light mesons using non-Abelian D-brane actions, revealing significant changes in meson spectra and providing a versatile framework for flavor dynamics in holography.

Contribution

It introduces improved methods for analyzing non-Abelian D-brane actions, leading to more accurate meson spectra and a general framework for flavor hierarchy modeling.

Findings

Scalar mesons become heavier with the new method

Vector mesons become lighter, removing previous degeneracy

Finite coupling effects alter meson mass dependence on quark masses

Abstract

We revisit the holographic description of heavy light mesons in the D3-D7 system at zero temperature, analyzing the dynamics of the coupled probe D7 branes through the non-Abelian Dirac-Born-Infeld action. Distinct quark masses are realized by separating the flavor branes, producing holographic flavor hierarchies. We refine the calculation made in previous works: we impose Hermiticity on the induced metric and fix the expansion of the determinant for matrix valued fields. Implementing these improvements yields modified fluctuation equations and quantitatively different meson spectra: the scalar modes become heavier while the vector modes become lighter, removing the degeneracy reported in the literature. At finite 't Hooft coupling, we also observe a qualitatively different dependence of the vector modes on the quark masses. The resulting prescription provides a consistent, broadly applicable framework for incorporating non-Abelian flavor dynamics into holographic models and can be readily extended to situations away from the vacuum.