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Register a new userThe large N limit of four dimensional Yang-Mills field coupled to adjoint fermions on a single site lattice
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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.
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We study the two-dimensional Yang--Mills theory with four supercharges in the large-$N$ limit. By using thermal boundary conditions, we analyze the internal energy and the distribution of scalars. We compare their behavior to the maximally supersymmetric case with sixteen supercharges, which is known to admit a holographic interpretation. Our lattice results for the scalar distribution show no visible dependence on $N$ and the energy at strong coupling appears independent of temperature.
We study four dimensional large-N SU(N) Yang-Mills theory coupled to adjoint overlap fermions on a single site lattice. Lattice simulations along with perturbation theory show that the bare quark mass has to be taken to zero as one takes the continuum limit in order to be in the physically relevant center-symmetric phase. But, it seems that it is possible to take the continuum limit with any renormalized quark mass and still be in the center-symmetric physics. We have also conducted a study of the correlations between Polyakov loop operators in different directions and obtained the range for the Wilson mass parameter that enters the overlap Dirac operator.
In K.~Hieda, A.~Kasai, H.~Makino, and H.~Suzuki, Prog. Theor. Exp. Phys. textbf{2017}, 063B03 (2017), a properly normalized supercurrent in the four-dimensional (4D) $mathcal{N}=1$ super Yang--Mills theory (SYM) that works within on-mass-shell correlation functions of gauge-invariant operators is expressed in a regularization-independent manner by employing the gradient flow. In the present paper, this construction is extended to the supercurrent in the 4D $mathcal{N}=2$ SYM. The so-constructed supercurrent will be useful, for instance, for fine tuning of lattice parameters toward the supersymmetric continuum limit in future lattice simulations of the 4D $mathcal{N}=2$ SYM.
Non-perturbative investigations of $mathcal N = 4$ supersymmetric Yang--Mills theory formulated on a space-time lattice have advanced rapidly in recent years. Large-scale numerical calculations are currently being carried out based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing. A recent development is the creation of an improved lattice action through a new procedure to regulate flat directions in a manner compatible with this supersymmetry, by modifying the moduli equations. In this proceedings I briefly summarize this new procedure and discuss the parameter space of the resulting improved action that is now being employed in numerical calculations.
We present some of the latest results from our numerical investigations of N=4 supersymmetric Yang--Mills theory formulated on a space-time lattice. Based on a construction that exactly preserves a single supersymmetry at non-zero lattice spacing, we recently developed an improved lattice action that is now being employed in large-scale calculations. Here we update our studies of the static potential using this new action, also applying tree-level lattice perturbation theory to improve the analysis of the potential itself. Considering relatively weak couplings, we obtain results for the Coulomb coefficient that are consistent with continuum perturbation theory.
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