We have simulated the SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. Such theories arise naturally in the context of composite Higgs models that include a partially composite top quark. We describe the low-lying meson spectrum of the theory and fit the pseudoscalar masses and decay constants to chiral perturbation theory. We infer as well the mass and decay constant of the Goldstone boson corresponding to the nonanomalous U(1) symmetry of the model. Our results are broadly consistent with large-N c scaling and vector-meson dominance.

We use lattice simulations to compute the baryon spectrum of SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. This model is closely related to a composite Higgs model in which the chimera baryon made up of fermions from both representations plays the role of a composite top-quark partner. The dependence of the baryon masses on each underlying fermion mass is found to be generally consistent with a quark-model description and large-N c scaling. We combine our numerical results with experimental bounds on the scale of the new strong sector to derive a lower bound on the mass of the top partner.

We study a lattice field theory model containing two flavors of massless staggered fermions with an onsite four-fermion interaction. The model contains a SU (4) symmetry which forbids nonzero fermion bilinear mass terms, due to which there is a massless fermion phase at weak couplings. However, even at strong couplings fermion bilinear condensates do not appear in our model, although fermions do become massive. While the existence of this exotic strongly coupled massive fermion phase was established long ago, the nature of the transition between the massless and the massive phase has remained unclear. Using Monte Carlo calculations in three space-time dimensions, we find evidence for a direct second order transition between the two phases suggesting that the exotic lattice phase may have a continuum limit at least in three dimensions. A similar exotic second order critical point was found recently in a bilayer system on a honeycomb lattice.

Using a simple three dimensional lattice four-fermion model we argue that massless fermions can become massive due to interactions without the need for any spontaneous symmetry breaking. Using large scale Monte Carlo calculations within our model, we show that this non-traditional mass generation mechanism occurs at a second order quantum critical point that separates phases with the same symmetries. Universality then suggests that the new origin for the fermion mass should be of wide interest.Comment: 11 pages, 20 figures (5 pages, 7 figures in the main paper and 6 pages, 13 figures in the supplementary material

Partial compositeness is a mechanism for the generation of fermion masses which replaces a direct Higgs coupling to the fermions by a linear mixing with heavy composite partners. We present the first calculation of the relevant matrix element in a lattice model which is very close to a candidate theory containing a composite Higgs boson and a partially composite top quark. Specifically, our model is an SU(4) gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations. The matrix element we obtain is small and hence our result disfavors the scenario of obtaining a realistic top mass in this model.