Quarkonium from the Fifth Dimension

TL;DR

This work analyzes quarkonium and generalized quarkonium in a holographic setup: N=4 Yang–Mills with fundamental matter introduced by D7-branes, studied at large 't Hooft coupling. By computing flavor, SO(4), and energy–momentum tensor form factors for spin-zero and spin-one hadrons, it reveals a universal finite transverse size $\sim m_h^{-1}$ across excitations, with distinctive large-$q^2$ and position-space behaviors governed by conformal symmetry. The results show that spin-≤1 states are surprisingly light and structurally different from QCD bound states, featuring vanishing anomalous magnetic and quadrupole form factors in the large-$\lambda$ limit and a core-plus-tail internal structure. These findings imply that strongly coupled holographic quarkonia have a characteristic scale set by $m_h = m_Q/\sqrt{\lambda}$, provide insights into how confinement and conformal dynamics shape hadron structure, and raise questions about the applicability of QCD intuition to such theories. The work also highlights methodological connections between bulk AdS/CFT computations, current matrix elements, and two-dimensional transverse charge distributions relevant for generalized parton distributions.

Abstract

Adding fundamental matter of mass m_Q to N=4 Yang Mills theory, we study quarkonium, and "generalized quarkonium" containing light adjoint particles. At large 't Hooft coupling the states of spin<=1 are anomalously light (Kruczenski et al., hep-th/0304032). We examine their form factors, and show these hadrons are unlike any known in QCD. By a traditional yardstick they appear infinite in size (as with strings in flat space) but we show that this is a failure of the yardstick. All of the hadrons are actually of finite size ~ \sqrt{g^2N}/m_Q, regardless of their radial excitation level and of how many valence adjoint particles they contain. Certain form factors for spin-1 quarkonia vanish in the large-g^2N limit; thus these hadrons resemble neither the observed J/Psi quarkonium states nor rho mesons.