Instanton bags, high density holographic QCD, and chiral symmetry restoration

We describe the simplest example of an instanton bag in Euclidean space. It consists of a monopole wall and a Kaluza-Klein monopole wall, lifted to one higher dimension, trapping the instanton charge in the middle. This object has finite instanton density in a three-dimensional volume. Baryon physics in holographic QCD models gets translated into a multi-instanton problem in the bulk, and a state with a high density baryonic charge consists of a nondiluted multi-instanton solution. The instanton bag is a good candidate for this high-density state. We compute its parameters via moduli stabilization. Chiral symmetry restoration is exhibited by this state, and it is a direct consequence of its nondiluted features.

Figure 1

Monopole wall.

Figure 2

Sequence of transformations from monopole wall to KK monopole wall, first the large-gauge transformation and then the $\pi$ rotation in the $x_3,x_4$ plane.

Figure 3

Monopole wall and KK monopole wall with instanton charge inside the two plates.

Figure 4

Web of string junctions in the $x_{3,4}$ plane. The basic constituent is the three string junction D1-F1-(1,1). The structure is periodic in the $x_3$ direction. The second is the web for the limit of coincident D1-strings. This configuration corresponds to the instanton bag of Fig. 3.

Figure 5

Check of the Chern-Simons flux.

Figure 6

Generic expectation for the energy density of the HQCD phases as function of instanton density $Q$.

Figure 7

Numerical plot of $\mathcal{E}(Q)$ for small values of $Q$ obtained from the minimization of (4.26) for $\mathrm{\Lambda }=2$. This confirms the expectation from the BPS approximation (4.9).

Figure 8

Numerical solution of $\mathcal{E}(Q)$ in a log-log plot for $\mathrm{\Lambda }=2$. This shows the interpolation between the almost-BPS limit for small $Q$ and the asymptotic solution (4.30) for large $Q$.

Figure 9

Geometric realization of confinement and chiral symmetry breaking in the Sakai-Sugimoto model and the embedded instanton bag on the $D8$’s worldvolume.

Figure 10

Charged particle tunneling a magnetic field strip.

Figure 11

Charged particle tunneling a “pure gauge” strip.