We study the gauge sector of Minimal Walking Technicolor, which is an SU(2) gauge theory with n f = 2 flavors of Wilson fermions in the adjoint representation. Numerical simulations are performed on lattices Nt × N 3 s , with Ns ranging from 8 to 16 and Nt = 2Ns, at fixed β = 2.25, and varying the fermion bare mass m0, so that our numerical results cover the full range of fermion masses from the quenched region to the chiral limit. We present results for the string tension and the glueball spectrum. A comparison of mesonic and gluonic observables leads to the conclusion that the infrared dynamics is given by an SU(2) pure Yang-Mills theory with a typical energy scale for the spectrum sliding to zero with the fermion mass. The typical mesonic mass scale is proportional to, and much larger than this gluonic scale. Our findings are compatible with a scenario in which the massless theory is conformal in the infrared. An analysis of the scaling of the string tension with the fermion mass towards the massless limit allows us to extract the chiral condensate anomalous dimension γ * , which is found to be γ * = 0.22 ± 0.06.

We investigate the structure and the novel emerging features of the mesonic nonsinglet spectrum of the minimal walking technicolor theory. Precision measurements in the nonsinglet pseudoscalar and vector channels are compared to the expectations for an IR-conformal field theory and a QCD-like theory. Our results favor a scenario in which minimal walking technicolor is (almost) conformal in the infrared, while spontaneous chiral symmetry breaking seems less plausible.

We discuss the lattice formulation of gauge theories with fermions in arbitrary representations of the color group and present in detail the implementation of the hybrid Monte Carlo (HMC)/rational HMC algorithm for simulating dynamical fermions. We discuss the validation of the implementation through an extensive set of tests and the stability of simulations by monitoring the distribution of the lowest eigenvalue of the Wilson-Dirac operator. Working with two flavors of Wilson fermions in the adjoint representation, benchmark results for realistic lattice simulations are presented. Runs are performed on different lattice sizes ranging from 4 3 Â 8 to 24 3 Â 64 sites. For the two smallest lattices we also report the measured values of benchmark mesonic observables. These results can be used as a baseline for rapid cross-checks of simulations in higher representations. The results presented here are the first steps toward more extensive investigations with controlled systematic errors, aiming at a detailed understanding of the phase structure of these theories, and of their viability as candidates for strong dynamics beyond the standard model.

In order to calculate QED corrections to hadronic physical quantities by means of lattice simulations, a coherent description of electrically-charged states in finite volume is needed. In the usual periodic setup, Gauss's law and large gauge transformations forbid the propagation of electrically-charged states. A possible solution to this problem, which does not violate the axioms of local quantum field theory, has been proposed by Wiese and Polley, and is based on the use of C boundary conditions. We present a thorough analysis of the properties and symmetries of QED in isolation and QED coupled to QCD, with C boundary conditions. In particular we learn that a certain class of electricallycharged states can be constructed in a fully consistent fashion without relying on gauge fixing and without peculiar complications. This class includes single particle states of most stable hadrons. We also calculate finite-volume corrections to the mass of stable charged particles and show that these are much smaller than in non-local formulations of QED.

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A strategy for computing theψψ anomalous dimension at the fixed point in infraredconformal gauge theories from lattice simulations is discussed. The method is based on the scaling of the spectral density of the Dirac operator or rather its integral, the mode number. It is relatively cheap, mainly for two reasons: (a) the mode number can be determined with quite high accuracy, and (b) theψψ anomalous dimension is extracted from a fit of several observables on the same set of configurations (no scaling in the Lagrangian parameters is needed). As an example theψψ anomalous dimension has been computed in the SU(2) theory with 2 Dirac fermions in the adjoint representation of the gauge group, and has been found to be γ * = 0.371 (20). In this particular case, the proposed strategy has proved to be very robust and effective.arXiv:1204.4432v3 [hep-lat]

We address the question of whether the large-N expansion in pure SUðNÞ gauge theories requires that k-string tensions must have a power series expansion in 1=N 2 , as in the sine law, or whether 1=N contributions are also allowable, as in Casimir scaling. We find that k-string tensions may, in fact, have 1=N corrections, and consistency with the large-N expansion in the open string sector depends crucially on an exact cancellation, which we will prove, among terms involving odd powers of 1=N in particular combinations of Wilson loops. It is shown how these cancellations are fulfilled, and consistency with the large-N expansion achieved, in a concrete example, namely, strong coupling lattice gauge theory with the heat-kernel action. This is a model which has both a 1=N 2 expansion and Casimir scaling of the k-string tensions. Analysis of the closed string channel in this model confirms our conclusions, and provides further insights into the large-N dependence of energy eigenstates and eigenvalues.

Abstract:The recent introduction of the gradient flow has provided a new tool to probe the dynamics of quantum field theories. The latest developments have shown how to use the gradient flow for the exploration of symmetries, and the definition of the corresponding renormalized Noether currents. In this paper we introduce infinitesimal translations along the gradient flow for gauge theories, and study the corresponding Ward identities. This approach is readily generalized to the case of gauge theories defined on a lattice, where the regulator breaks translation invariance. The Ward identities in this case lead to a nonperturbative renormalization of the energy-momentum tensor. We discuss an application of this method to the study of dilatations and scale invariance on the lattice.