Higher representations on the lattice: numerical simulations. SU(2) with   adjoint fermions
  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 HMC/RHMC 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 4^3x8 to 24^3x64 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 towards 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. 
Luigi Del Debbio, Agostino Patella, Claudio Pica