Holographic mesons in various dimensions

TL;DR

This work uses gauge/gravity duality with flavor branes to compute the meson spectra of strongly coupled SYM theories in various dimensions, by analyzing fluctuations of probe Dk-branes in near-horizon Dp-brane backgrounds. A central result is the universal scaling M^2 ~ m_q^{5-p}/(g_{YM}^2 N) times a dimensionless eigenvalue, which translates to M ~ m_q / g_{eff}(m_q) with g_{eff}^2(m_q)= g_{YM}^2 N m_q^{p-3}, applicable across multiple Dp/Dk configurations and defect constructions. Analytically tractable cases (notably p=3) reveal hypergeometric solutions and degeneracies tied to conformal symmetry, while generic cases rely on numerical ODE solutions. The paper also explores strong-coupling regimes beyond ten-dimensional supergravity via M-theory uplifts, showing consistent holographic distance-energy relations and supporting the robustness of the meson-mass scaling in both intermediate and infrared limits. Overall, the results reinforce the interpretation that holography fixes the energy scales of meson spectra through the radial/energy correspondence, with potential implications for holographic QCD-like models and defect theories.

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.