Large-Nreduction in QCD with two adjoint Dirac 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, am, and look for the region where the Z 4 N 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. D 80: 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 Ndependence of the width of this region and find strong evidence that it remains of finite width as N → ∞. 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 N = ∞, apply also for the large volume theory, which is minimal walking technicolor at N = ∞. We find a first-order transition as a function of am 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.

Confinement in large N gauge theories

“…One or two flavours of overlap fermions have been studied by Hietanen and Narayanan [25]. Other authors [26]- [27] use Wilson fermions. In all cases they show evidence that Z(N) 4 symmetry is preserved for a certain range of quark masses and values of N.…”

Neutral bions in the ℂ $$ \mathbb{C} $$ P N −1 model

“…This confinement mechanism may remain responsible for the confinement at strong-coupling regime due to the continuity principle. This argument is also of importance in terms of the recent progress in large-N volume reduction [30][31][32][33][34][35][36][37][38][39][40]. On the other side, neutral bions (zero topological charge and zero magnetic charge) can be identified as the infrared renormalon [10][11][12][13][14][15][16][17][18][19][41][42][43].…”

Weak-coupling analysis of the single-site large-Ngauge theory coupled to adjoint fermions

“…Numerical studies with two flavors of Wilson fermions (both massless and massive) were carried out in [24]. From Fig.…”

“…The ordering of the operators will matter at finite lattice coupling if more than two of the k µ are non-zero. We do not have the gauge field data for Wilson fermions used in [24] but we do have them for massless overlap fermions at b = 0.65, f = 1 and m w = −4 in [25]. The results for c k (b) are plotted in Fig.…”

“…Furthermore, the coefficients with small k could be accidentally small. This suggests that the conclusions in [24] possibly result from being far away from the weak-coupling limit and not looking at a sufficient number of Fourier modes. In addition, we can also conclude that we cannot use a single-site model with heavy Wilson fermions and obtain the continuum limit of a pure gauge theory in contrast to the claims made in [26].…”