Baryons and Flux Tubes in Confining Gauge Theories from Brane Actions

TL;DR

The paper addresses how baryons arise in large-$N$ confining gauge theories by holographically modeling them as D5- or D4-branes wrapped on spheres and terminating fundamental strings in non-extremal D3/D4 backgrounds. Using the Born-Infeld plus Wess-Zumino worldvolume action, it derives and analyzes embedding solutions that describe both point-like and split baryons, revealing a confining color flux tube whose tension depends nontrivially on the quark fraction $ν$. In three dimensions, the flux-tube tension is given by $\sigma_3(ν)$ with a characteristic $ u$-dependence, while the four-dimensional case yields a simple $ u(1- u)$ dependence, illustrating how the flavor content is encoded in the brane embedding via the angular coordinates. These holographic results provide a concrete, calculable picture of baryon structure in confining gauge theories and suggest extensions to finite-temperature setups and alternative gravity duals.

Abstract

We study baryon configurations in large N non-supersymmetric SU(N) gauge theories, applying the AdS/CFT correspondence. Using the D5-brane worldvolume theory in the near-horizon geometry of non-extremal D3-branes, we find embeddings which describe baryonic states in three-dimensional QCD. In particular, we construct solutions corresponding to a baryon made of N quarks, and study what happens when some fraction $ν$ of the total number of quarks are bodily moved to a large spatial separation from the others. The individual clumps of quarks are represented by Born-Infeld string tubes obtained from a D5-brane whose spatial section has topology $R \times S^4$. They are connected by a confining color flux tube, described by a portion of the fivebrane that runs very close and parallel to the horizon. We find that this flux tube has a tension with a nontrivial $ν$-dependence (not previously obtained by other methods). A similar picture is presented for the four-dimensional case.

Figures (6)

• Figure 1: The potential $V(\theta)=-\left[D(\theta)^2+\sin^8\theta\right]$ for $\nu=0,1/4,1/2$ (see text for discussion).
• Figure 2: Family of solutions illustrating the progressive deformation of the fivebrane by the bundle of $N$ fundamental strings. The dotted circle represents the horizon. The stable configuration is a 'tube' with $r_{0}\to\infty$.
• Figure 3: The three-dimensional projection of the D5-brane. Every point on the curve is an ${\bf S}^{4}$. One can clearly see how the brane drops down towards the horizon, extends horizontally along it, and finally leaves at the other end. From the point of view of the three-dimensional $SU(N)$ gauge theory, which lives in the $\{x,y,z\}$ directions, this configuration represents a baryon split into two groups of $\nu N$ and $(1-\nu)N$ quarks (the vertical segments --- see Fig. \ref{['splitpol']}), connected by a flux tube extending a finite distance along the $x$ direction.
• Figure 4: Polar plot of $r(\theta)$ -- the two-dimensional projection of Fig. \ref{['split3d']}. The Born-Infeld string 'tubes' pointing up and down represent two groups of $\nu N$ and $(1-\nu)N$ quarks, respectively (with $\nu=0.9$ here). The brane extends in the $x$-direction mostly at the inflection point (the cusp), while $x$ is essentially constant along the tubes.
• Figure 5: The tension of the flux tube (normalized to unity at its peak) as a function of $\nu$, the fraction of quarks pulled apart. In the full theory $\nu$ should be quantized in units of ${1/N}$. See text for discussion.