Dynamics of Baryons from String Theory and Vector Dominance

TL;DR

This work embeds baryons in the Sakai–Sugimoto holographic QCD framework, modeling them as small instanton solitons in a five-dimensional $U(N_F)$ gauge theory on D8-branes. Through a systematic dimensional reduction, the authors derive a 5D effective action for a nucleon field that couples to the entire vector-tensor meson tower via both minimal and magnetic interactions, leading to a fully vector-dominated electromagnetic structure in 4D. They show that axial and vector couplings, as well as anomalous magnetic moments, arise with controlled large-$N_c$ and large-$\lambda$ scaling, and they provide numerical estimates that agree reasonably with experimental values after a modest $N_c\to N_c+2$ shift motivated by collective quantization. The results unify meson-baryon interactions and EM form factors within a single holographic description, highlighting vector dominance as a natural outcome of the tower of vector mesons and offering predictions for nucleon couplings and radii while acknowledging extrapolation caveats to real-world QCD.

Abstract

We consider a holographic model of QCD from string theory, a la Sakai and Sugimoto, and study baryons. In this model, mesons are collectively realized as a five-dimensional \$U(N_F)=U(1)\times SU(N_F)$ Yang-Mills field and baryons are classically identified as $SU(N_F)$ solitons with a unit Pontryagin number and $N_c$ electric charges. The soliton is shown to be very small in the large 't Hooft coupling limit, allowing us to introduce an effective field ${\cal B}$. Its coupling to the mesons are dictated by the soliton structure, and consists of a direct magnetic coupling to the $SU(N_F)$ field strength as well as a minimal coupling to the $U(N_F)$ gauge field. Upon the dimensional reduction, this effective action reproduces all interaction terms between nucleons and an infinite tower of mesons in a manner consistent with the large $N_c$ expansion. We further find that all electromagnetic interactions, as inferred from the same effective action via a holographic prescription, are mediated by an infinite tower of vector mesons, rendering the baryon electromagnetic form factors completely vector-dominated as well. We estimate nucleon-meson couplings and also the anomalous magnetic moments, which compare well with nature.

Figures (3)

• Figure 1: Plot of $g_{A,min}$ versus $\lambda N_c$.
• Figure 2: (a) Photon coupling to the nucleon via vector meson $V$ and (b) direct photon coupling to the nucleon. The blob represents the intrinsic form factor accounting for short-distance effects (referred to as "intrinsic core" in some circles) unaccounted for in the effective theory, e.g., asymptotically free QCD property.
• Figure 3: The Sachs form factors vs. $q^2$ in ${\rm GeV}^2$: B=$G_M^p$, C=$G_E^p$, D=$G_M^n$, and E=$G_E^n$, where we take $m_B=M_{KK}$ and have shifted $N_C\to N_C+2$.