Non-perturbative volume-reduction of large-N QCD with adjoint fermions

TL;DR

The paper tests nonperturbative volume reduction for large-$N$ QCD with adjoint fermions by simulating the single-site AEK model and mapping the center-symmetry realization in the $(b,\kappa)$ plane. Using Wilson actions and a robust set of center- and symmetry-sensitive observables, the study identifies a broad funnel where the $(Z_N)^4$ center symmetry remains unbroken, supporting the reduction conjecture and its equivalence to infinite-volume adjoint QCD at large $N$. Physical probes such as the average plaquette and Dirac-spectrum diagnostics indicate proximity to large-$N pure-gauge behavior in selected parameter regions, though the epsilon-regime remains out of reach at the tested $N$. The work lays groundwork for applying volume reduction to study long-distance large-$N$ phenomena, while pointing to the need for larger $N$ and improved algorithms to access deeper infrared physics and the continuum limit.

Abstract

We use nonperturbative lattice techniques to study the volume-reduced "Eguchi-Kawai" version of four-dimensional large-N QCD with a single adjoint Dirac fermion. We explore the phase diagram of this single-site theory in the space of quark mass and gauge coupling using Wilson fermions for a number of colors in the range 8 <= N <= 15. Our evidence suggests that these values of N are large enough to determine the nature of the phase diagram for N-->oo. We identify the region in the parameter space where the (Z_N)^4 center-symmetry is intact. According to previous theoretical work using the orbifolding paradigm, and assuming that translation invariance is not spontaneously broken in the infinite-volume theory, in this region volume reduction holds: the single-site and infinite-volume theories become equivalent when N-->oo. We find strong evidence that this region includes both light and heavy quarks (with masses that are at the cutoff scale), and our results are consistent with this region extending towards the continuum limit. We also compare the action density and the eigenvalue density of the overlap Dirac operator in the fundamental representation with those obtained in large-N pure-gauge theory.

Figures (23)

• Figure 1: Conjectured phase diagram in the $\kappa-b$ plane for a QCD-like theory with a single Dirac adjoint fermion. Details are discussed in the text.
• Figure 2: Conjectured phase diagram for the single-site model in the large-$N$ limit. Details are discussed in the text.
• Figure 3: Scatter plots of the four Polyakov loops for $N=10$ and $\kappa=0$.The values of the coupling are $b=10^{-6}$ (left), $b=0.3421$ (middle) and $b=0.5$ (right).
• Figure 4: Plot of the average plaquette ([blue] pluses) and the magnitude of the Polyakov loop $P_{\mu=1}$ ([red] crosses) at $\kappa=0$ as a function of $b$ for $N=10$.
• Figure 5: Scatter plots of the four Polyakov loops for $b=0.3$ and $N=10$, The value of $\kappa$ increases from the top-left plot to the bottom-right plot in the order $0.01$, $0.03$, $0.06$, $0.11$, $0.165$, and $0.185$.