We report preliminary results on the finite temperature behavior of SU(4) gauge theory with dynamical quarks in both the fundamental and two-index antisymmetric representations. This system is a candidate to present scale separation behavior, where fermions in different representations condense at different temperature or coupling scales. Our simulations, however, reveal a single finite-temperature phase transition at which both representations deconfine and exhibit chiral restoration. It appears to be strongly first order. We compare our results to previous single-representation simulations. We also describe a Pisarski-Wilczek stability analysis, which suggests that the transition should be first order.

B. Svetitsky,

Models for what may lie behind the Standard Model often require non-perturbative calculations in strongly coupled field theory. This creates opportunities for lattice methods, to obtain quantities of phenomenological interest as well as to address fundamental dynamical questions. I survey recent work in this area.

T. DeGrand, D. Hackett, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these “chimera baryons” has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models in which the top quark is partially composite.

T. DeGrand, M. Golterman, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

The SU(4) gauge theory with two flavors of Dirac fermions in the sextet representation shares features of a candidate for a composite Higgs model. The analogue of the Higgs multiplet of the Standard Model lives in the Goldstone manifold resulting from spontaneous breaking of the global symmetry SU(4) to SO(4). The Higgs potential arises from interaction with the particles of the Standard Model. We have computed the gauge boson contribution to the Higgs potential, using valence overlap fermions on a Wilson-clover sea. The calculation is similar to that of the electromagnetic mass splitting of the pion multiplet in QCD.

T. DeGrand, M. Golterman, W. I. Jay, E. T. Neil, Y. Shamir, and B. Svetitsky,

We develop methods to calculate the electroweak gauge boson contribution to the effective Higgs potential in the context of composite Higgs models, using lattice gauge theory. The calculation is analogous to that of the electromagnetic mass splitting of the pion multiplet in QCD. We discuss technical details of carrying out this calculation, including modeling of the momentum and fermion-mass dependence of the underlying current-current correlation function; direct integration of the correlation function over momentum; and fits based on the minimal-hadron approximation. We show results of a numerical study using valence overlap fermions, carried out in an SU(4) gauge theory with two flavors of Dirac fermions in the two-index antisymmetric representation.

T. DeGrand, Y. Liu, E. T. Neil, Y. Shamir, and B. Svetitsky,

We present a first look at the spectroscopy of SU(4) gauge theory coupled to two flavors of Dirac fermions in the two-index antisymmetric representation, which is a real representation. We compute meson and diquark masses, the pseudoscalar and vector meson decay constants, and the masses of six-quark baryons. We make comparisons with large-Nexpectations._{c}

T. DeGrand, Y. Liu, E. T. Neil, Y. Shamir, and B. Svetitsky, Spectroscopy of SU(4) lattice gauge theory with fermions in the two index anti-symmetric representation, talk given by Y. Liu at Lattice 2014, the 32nd International Symposium on Lattice Field Theory, Columbia University, New York, NY, June 2014, published in proceedings, Proc. Sci. (LATTICE2014) 275 (arXiv:1412.4851 [hep-lat], December 2014).

We present a study of spectroscopy of SU(4) lattice gauge theory coupled to two flavors of Dirac fermions in the anti-symmetric two index representation. The fermion representation is real, and the pattern of chiral symmetry breaking is SU(2N) → SO(2_{f }N) with_{f }Nflavors of Dirac fermions. It is an interesting generalization of QCD, for several reasons: it allows direct exploration of an alternate large_{f }Nexpansion, it can be simulated at non-zero chemical potential with no sign problem, and several UV completions of composite Higgs systems are built on it. We present preliminary results on the baryon and meson spectra of the theory and compare them with SU(3) results and with expectations for large_{c}-Nscaling._{c}

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