Holographic mesons in various 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.