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Register a new userThe three-loop beta-function of SU(N) lattice gauge theories with overlap fermions
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We briefly report our calculation of the 2-loop coefficient of the coupling constant renormalization function Z_g in lattice perturbation theory. The quantity under study is defined through g_0 = Z_g g, where g_0 (g) is the bare (renormalized) coupling constant. The 2-loop expression for Z_g can be directly related to the 3-loop bare beta-function beta_L(g_0). Our calculation is performed using overlap fermions and Wilson gluons, and the background field technique has been chosen for convenience. Our results depend explicitly on the number of fermion flavors (N_f) and colors (N). Since the dependence of Z_g on the overlap parameter rho cannot be extracted analytically, we tabulate our results for different values of rho in the allowed range (0<rho<2), focusing on values which are being used most frequently in simulations. Plots of the 1- and 2-loop results for Z_g versus rho exhibit a nontrivial dependence on the overlap parameter. A longer write-up of this work may be found in 0709.4368.
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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.
We consider three-dimensional lattice SU($N_c$) gauge theories with multiflavor ($N_f>1$) scalar fields in the adjoint representation. We investigate their phase diagram, identify the different Higgs phases with their gauge-symmetry pattern, and determine the nature of the transition lines. In particular, we study the role played by the quartic scalar potential and by the gauge-group representation in determining the Higgs phases and the global and gauge symmetry-breaking patterns characterizing the different transitions. The general arguments are confirmed by numerical analyses of Monte Carlo results for two representative models that are expected to have qualitatively different phase diagrams and Higgs phases. We consider the model with $N_c = 3$, $N_f=2$ and with $N_c=2$, $N_f= 4$. This second case is interesting phenomenologically to describe some features of cuprate superconductors.
We compare SU(2) Polyakov loop models with different effective actions with data from full two-color QCD simulations around and above the critical temperature. We then apply the effective theories at finite temperature and density to extract quantities like Polyakov loop correlators, effective Polyakov loop potentials and baryon density.
As a part of the project studying large $N_f$ QCD, the LatKMI Collaboration has been investigating the SU(3) gauge theory with four fundamental fermions (four-flavor QCD). The main purpose of studying four-flavor QCD is to provide a qualitative comparison to $N_f= 8$, $12$, $16$ QCD; however, a quantitative comparison to real-world QCD is also interesting. To make such comparisons more meaningful, it is desirable to use the same kind of lattice action consistently, so that qualitative difference of different theories are less affected by artifacts of lattice discretization. Here, we adopt the highly-improved staggered quark action with the tree-level Symanzik gauge action (HISQ/tree), which is exactly the same as the setup for our simulations for $SU(3)$ gauge theories with $N_f=8$, $12$ and $16$ fundamental fermions~cite{Aoki:2013xza, Aoki:2012eq, Aoki:2014oma}. In the next section, we show the fermion mass dependence of $F_pi$, $langlebar{psi}psirangle$, $M_pi$, $M_rho$, $M_N$ and their chiral extrapolations. In section 3, preliminary results of the measurement of the mass of the flavor-singlet scalar bound state will be reported.
We study the discrete beta function of SU(3) gauge theory with Nf=12 massless fermions in the fundamental representation. Using an nHYP-smeared staggered lattice action and an improved gradient flow running coupling $tilde g_c^2(L)$ we determine the continuum-extrapolated discrete beta function up to $g_c^2 approx 8.2$. We observe an IR fixed point at $g_{star}^2 = 7.3left(_{-2}^{+8}right)$ in the $c = sqrt{8t} / L = 0.25$ scheme, and $g_{star}^2 = 7.3left(_{-3}^{+6}right)$ with c=0.3, combining statistical and systematic uncertainties in quadrature. The systematic effects we investigate include the stability of the $(a / L) to 0$ extrapolations, the interpolation of $tilde g_c^2(L)$ as a function of the bare coupling, the improvement of the gradient flow running coupling, and the discretization of the energy density. In an appendix we observe that the resulting systematic errors increase dramatically upon combining smaller $c lesssim 0.2$ with smaller $L leq 12$, leading to an IR fixed point at $g_{star}^2 = 5.9(1.9)$ in the c=0.2 scheme, which resolves to $g_{star}^2 = 6.9left(_{-1}^{+6}right)$ upon considering only $L geq 16$. At the IR fixed point we measure the leading irrelevant critical exponent to be $gamma_g^{star} = 0.26(2)$, comparable to perturbative estimates.
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