Holographic mesons in various dimensions

TL;DR

This paper computes the mesonic spectra in various dimensions using holography, revealing a universal discrete spectrum deeply bound by a scale set by quark mass and effective coupling, with implications for infrared behavior in SYM theories.

Contribution

It provides a unified holographic analysis of meson spectra across different dimensions, including the transition to M-theory in the infrared.

Findings

Spectrum is discrete and deeply bound.

Mass gap scales with quark mass and effective coupling.

Universal behavior across different dimensions.

Abstract

We calculate the spectrum of fluctuations of a probe Dk-brane in the background of N Dp-branes, for k=p,p+2,p+4 and p< 5. The result corresponds to the mesonic spectrum of a (p+1)-dimensional super-Yang-Mills (SYM) theory coupled to `dynamical quarks', i.e., fields in the fundamental representation -- the latter are confined to a defect for k=p and p+2. We find a universal behaviour where the spectrum is discrete and the mesons are deeply bound. The mass gap and spectrum are set by the scale M ~ m_q/g_{eff}(m_q), where m_q is the mass of the fundamental fields and g_{eff}(m_q) is the effective coupling evaluated at the quark mass, i.e. g_{eff}^2(m_q)=g_{ym}^2 N m_q^{p-3}. We consider the evolution of the meson spectra into the far infrared of three-dimensional SYM, where the gravity dual lifts to M-theory. We also argue that the mass scale appearing in the meson spectra is dictated by holography.