The large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice

TL;DR

This work probes whether volume reduction via Eguchi–Kawai-type ideas extends to four-dimensional SU($N$) Yang–Mills theory with adjoint fermions on a single-site lattice, contrasting naive and overlap fermion discretizations. Through a combination of weak-coupling analysis and Hybrid Monte Carlo simulations, it demonstrates that $Z_N^4$ center symmetries are broken by naive fermions but preserved by overlap fermions, supporting the viability of single-site reduction with overlap fermions. The study also provides evidence for a nonzero chiral condensate for $f=\tfrac12$ and $f=1$ at a fixed lattice coupling, with low-lying Dirac spectra in agreement with chiral random matrix theory for the symplectic ensemble. Collectively, the results establish a concrete path to lattice investigations of large-$N$ gauge dynamics on a single site and connect center-symmetry realization with chiral properties and potential infrared behavior.

Abstract

We consider the large N limit of four dimensional SU(N) Yang-Mills field coupled to adjoint fermions on a single site lattice. We use perturbative techniques to show that the Z^4_N center-symmetries are broken with naive fermions but they are not broken with overlap fermions. We use numerical techniques to support this result. Furthermore, we present evidence for a non-zero chiral condensate for one and two Majorana flavors at one value of the lattice gauge coupling.

Figures (13)

• Figure 1: Naïve fermions: Plot of $P_\mu$ as a function of $f$ for three different choices of $(\beta ,N)$ and $\mu=0.01$.
• Figure 2: Naïve fermions: Plot of $P_\mu$ as a function of $f$ at $N=23$, $\beta=4$, and $\mu=0.01$.
• Figure 3: Naïve fermions: Plot of smallest eigenvalue, $\lambda(p)$ with $p_\mu=\left(\theta_\mu^i-\theta_\mu^j\right)$ and $i\ne j$, for $N=23$, $\beta=4$, and $\mu=0.01$.
• Figure 4: Overlap fermions: Plot of $P_\mu$ as a function of $f$ at $N=23$, $\beta=1$, $m=5$, and $\mu=0.01$.
• Figure 5: Overlap fermions: Plot of $P_\mu$ as a function of $m$ at $N=23$, $\beta=1$, and $\mu=0.01$ for two different values of $f$.