Field theory as a tool to constrain new physics models

One of the major problems in developing new physics scenarios is that very often the parameters can be adjusted such that in perturbation theory almost all experimental low-energy results can be accommodated. It is therefore desirable to have additional constraints. Field-theoretical considerations can provide such additional constraints on the low-lying spectrum and multiplicities of models. Especially for theories with elementary or composite Higgs particle the Fr\"ohlich-Morchio-Strocchi mechanism provides a route to create additional conditions, though showing it to be at work requires genuine non-perturbative calculations. The qualitative features of this procedure are discussed for generic 2-Higgs-doublet models, grand-unified theories, and technicolor-type theories.Comment: 5 page

Scalar-matter-gluon interaction

A full non-perturbative treatment of gauge theories requires to include matter fields on equal footing with the gauge fields. Scalar matter can act as a role model for generic matter, as many questions, e.g. confinement, can be posed without referring to a particular Lorentz structure. Due to their rather simple structure they are also useful to develop methods. One possible way to describe gauge theories beyond perturbation theory is based on correlation functions. After a short discussion of the setup, lattice gauge theory is used to analyze the interaction of gluons with quenched fundamental and adjoint scalars. Both the two-point and three-point correlation functions for massive and massless adjoint and fundamental scalars will be determined, in minimal Landau gauge. The findings are in agreement with the possibility that scalars are only slightly affected by the interaction with gluons. The results are compared briefly with dynamical, massive scalars, showing no significant changes in the confinement region compared to the quenched case.Comment: 10 pages, 3 figures, invited talk presented at the workshop "The many faces of QCD", Ghent, Belgium, 1st of November-5th of November 2010; submitted to the proceeding

Gauge engineering and propagators

Beyond perturbation theory gauge-fixing becomes more involved due to the Gribov-Singer ambiguity: The appearance of additional gauge copies requires to define a procedure how to handle them. For the case of Landau gauge the structure and properties of these additional gauge copies will be investigated. Based on these properties gauge conditions are constructed to account for these gauge copies. The dependence of the propagators on the choice of these complete gauge-fixings will then be investigated using lattice gauge theory for Yang-Mills theory. It is found that the implications for the infrared, and to some extent mid-momentum behavior, can be substantial. In going beyond the Yang-Mills case it turns out that the influence of matter can generally not be neglected. This will be briefly discussed for various types of matter.Comment: 9 pages, 4 figures, Conference: XIIth Quark Confinement and the Hadron Spectrum, August 28-September 04, 2016, Thessaloniki, Greece, submitted to the proceeding

Local and global gauge-fixing

Gauge-fixing as a sampling procedure of gauge copies provides a possibility to construct well-defined gauges also beyond perturbation theory. The implementation of such sampling strategies in lattice gauge theory is briefly outlined, and examples are given for non-perturbative extensions of the Landau gauge. An appropriate choice of sampling can also introduce non-trivial global symmetries as a remainder of the gauge symmetry. Some examples for this are also given, highlighting their particular advantages.Comment: 8 pages, 1 figure, invited talk presented at the conference "Quark Confinement and the Hadron Spectrum X", Munich, Germany, 8th-12th of October 2012; submitted to the proceeding