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QCD domain walls, Chern-Simons theories and holography

Riccardo Argurio, Matteo Bertolini, Francesco Bigazzi, Aldo L. Cotrone, Pierluigi Niro

TL;DR

The paper investigates domain walls in massive QCD at $\theta=\pi$ using the Witten-Sakai-Sugimoto holographic model. It shows that wall dynamics reproduce QCD expectations and that a three-dimensional Chern-Simons theory with fundamental scalars captures the wall physics at the phase transition between small- and large-mass regimes, with tachyon condensation on D6/D8 strings providing the mechanism. The results support a holographic realization of the proposed 3d dual descriptions and level-rank relations on domain walls, reinforcing the connection between 4d QCD dynamics and 3d defect theories. The work highlights the utility of string-theoretic embeddings to illuminate defect dynamics and phase structure in strongly coupled gauge theories.

Abstract

Massive QCD at $θ=π$ breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are supported by the string theory construction.

QCD domain walls, Chern-Simons theories and holography

TL;DR

The paper investigates domain walls in massive QCD at using the Witten-Sakai-Sugimoto holographic model. It shows that wall dynamics reproduce QCD expectations and that a three-dimensional Chern-Simons theory with fundamental scalars captures the wall physics at the phase transition between small- and large-mass regimes, with tachyon condensation on D6/D8 strings providing the mechanism. The results support a holographic realization of the proposed 3d dual descriptions and level-rank relations on domain walls, reinforcing the connection between 4d QCD dynamics and 3d defect theories. The work highlights the utility of string-theoretic embeddings to illuminate defect dynamics and phase structure in strongly coupled gauge theories.

Abstract

Massive QCD at breaks CP spontaneously and admits domain walls whose dynamics and phases depend on the number of flavors and their masses. We discuss these issues within the Witten-Sakai-Sugimoto model of holographic QCD. Besides showing that this model reproduces all QCD expectations, we address two interesting claims in the literature. The first is about the possibility that the QCD domain-wall theory is fully captured by three-dimensional physics, only. The second regards the existence of quantum phases in certain Chern-Simons theories coupled to fundamental matter. Both claims are supported by the string theory construction.

Paper Structure

This paper contains 8 sections, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Witten-Sakai-Sugimoto model
  3. Domain walls of pure Yang-Mills
  4. Domain walls of massive QCD
  5. Small quark mass regime
  6. Large quark mass regime and the phase transition
  7. Conclusions and outlook
  8. Witten background

Figures (2)

  • Figure 1: Domain walls of massive QCD at $\theta=\pi$ and their phases in the complex $m^{N_f} e^{i\theta}$ plane, including the proposed three-dimensional CS theories describing them. On the left, QCD with $N_f=1$; on the right, QCD with $1 < N_f < N_{CFT}$. The blue line represents the values of quark masses for which the domain wall exists. At $m_{tr} \sim \Lambda$ a phase transition occurs. The DW ceases to exist at $m=m_0$ and $m=0$ for $N_f=1$ and $N_f>1$, respectively.
  • Figure 2: Flavors and domain walls in the Witten-Sakai-Sugimoto model. The flavor D8/$\overline{\hbox{D8}}$-branes are placed at fixed antipodal point on the $S_{x_4}$ circle and extend in the transverse radial direction. The D6-branes sit at the tip of the cigar geometry.