Hadron Masses and Screening from AdS Wilson Loops

TL;DR

The paper addresses string breaking and color screening in a strongly coupled gauge theory with dynamical quarks by employing the AdS/CFT correspondence with $N=4$ SYM plus flavors introduced via D7 branes. The authors compute Wilson loops holographically using a Legendre-transformed string action and compare two competing configurations, revealing that the heavy–light binding energy becomes an order-one multiple of the light-quark mass $m$ and is independent of the coupling $g^2 N$ at large $g^2 N$, with a screening length $L_{sc} \sim 2 \sqrt{g_{YM}^2 N}/m$. They further show that meson–meson interactions in the D7 flavor setup proceed via pion exchange with $m_{\pi} \sim O(1) \times m$, yielding exponentially suppressed long-range forces, while the D3-brane (W-boson) scenario exhibits Coulomb behavior from massless exchange. Overall, the work provides a gravity-dual picture of string snapping and color screening in a flavor-rich holographic theory, offering qualitative insights into QCD-like dynamics and a framework for exploring flavor effects in strongly coupled systems.

Abstract

We show that in strongly coupled N=4 SYM the binding energy of a heavy and a light quark is independent of the strength of the coupling constant. As a consequence we are able to show that in the presence of light quarks the analog of the QCD string can snap and color charges are screened. The resulting neutral mesons interact with each other only via pion exchange and we estimate the masses

Figures (4)

• Figure 1: Quark-antiquark potential in a confining gauge theory with dynamical fundamental matter. After an initial linear rise the potential plateaus at twice the mass of the lightest hadron.
• Figure 2: Quark-antiquark potential between two heavy test quarks of mass $M$ in a conformal field theory in the presence of a dynamical quark of mass $m$. At weak coupling the binding energy is less than the mass of the dynamical quark and hence the potential is Coulomb all the way. If the binding energy becomes bigger than $m$ one finds a crossover from Coulomb behavior to a constant.
• Figure 3: The two classical configurations contributing to the expectation value of the Wilson line in the presence of dynamical quarks.
• Figure 4: The flux dual to the meson-meson potential for a dynamical HM from D7 branes and a dynamical W-boson from D3 branes respectively. In latter case the flux is confined to a plane and bound to give rise to a Coulomb force. In the former the flux can make use of the AdS geometry and leads to no long range force.