Large-N reduction in QCD with two adjoint Dirac fermions

TL;DR

This study extends large-N volume reduction to QCD-like theories with two adjoint Dirac fermions by analyzing a single-site Adjoint Eguchi-Kawai model. Using Hybrid Monte Carlo simulations up to $N=53$, the authors map a phase diagram in the $(\kappa,b)$ plane and identify a broad funnel with unbroken $Z_N^4$ center symmetry, within which the single-site theory is conjectured to be equivalent to the large-volume theory as $N\to\infty$. They report a first-order transition in the hopping parameter $\kappa$ and observe finite-$N$ corrections dominated by $1/N$ terms, with the funnel width remaining finite in the large-$N$ limit, suggesting reduction can yield physical observables for the large-volume theory, including the minimal walking technicolor scenario at $N=\infty$. The work also analyzes the spectrum of the Wilson-Dirac operator, its hermitian square $Q^2$, and large Wilson loops to assess the viability of extracting the heavy-quark potential and other observables from reduced models, highlighting both opportunities and limitations of this approach for lattice gauge theories with adjoint fermions.

Abstract

We use lattice simulations to study the single-site version of SU(N) lattice gauge theory with two flavors of Wilson-Dirac fermions in the adjoint representation, a theory whose large volume correspondent is expected to be conformal or nearly conformal. Working with N as large as 53, we map out the phase diagram in the plane of bare `t Hooft coupling, g^2 N, and of the lattice quark mass, a*m, and look for the region where the Z_N^4 center symmetry of the theory is intact. In this region one expects the large-N equivalence of the single site and infinite volume theories to be valid. As for the N_f=1 case (see Phys. Rev. D80: 065031), we find that the center-symmetric region is large and includes both light fermion masses and masses at the cutoff scale. We study the N-dependence of the width of this region and find strong evidence that it remains of finite width as N goes to infinity. Simulating with couplings as small as g^2 N = 0.005, we find that the width shrinks slowly with decreasing g^2 N, at a rate consistent with analytic arguments. Within the center-symmetric region our results for the phase structure, when extrapolated to infinite N, apply also for the large volume theory, which is minimal walking technicolor with N=infinity. We find a first-order transition as a function of a*m for all values of b, which we argue favors that the theory is confining in the infrared. Finally, we measure the eigenvalue densities of the Wilson-Dirac operator and its hermitian version, and use large Wilson loops to study the utility of reduction for extracting physical observables.

Figures (22)

• Figure 1: Average number of CG iterations in the MD updates for various $N$ as a function of $\kappa$ at $b=1.0$. Results are from UP scans.
• Figure 2: Sketch of phase diagram for the $N_f=2$ AEK model in the $\kappa-b$ plane for $N\approx 30$. Note that the $\kappa=0$ axis is the EK model. The positions of phase boundaries are approximate, and depend somewhat on $N$. The shaded region at $\kappa_c$ indicates the uncertainty in the position of what appears to be a first-order transition due to hysteresis. Within each region we note the subset of the $Z_N^4$ center symmetry that is unbroken, with $Z_1$ indicating complete breakdown. The center symmetry is unbroken in the hysteresis region. The detailed symmetry-breaking pattern for large $\kappa$ is representative, and depends to some extent on $N$. For further discussion, see text.
• Figure 3: Scans (both UP and DOWN) of the average plaquette at $b=1.0$ for $N=16$ and $30$. The results of an extrapolation to $N=\infty$ (described in the text) are shown in the central region.
• Figure 4: As for Fig. \ref{['fig:scan_b1.0']} but for $b=0.5$.
• Figure 5: Scans of the absolute values of corner variables for $b=1.0$, for $N=16$ and $30$. Results for the 12 independent $|M_{\mu\nu}|$'s are shown separately.