A model for gauge theories with Higgs fields

TL;DR

This paper introduces a simple bosonic quantum field theory model that captures key features of gauge theories with Higgs fields, including asymptotic freedom, mass generation, and complex quantum phenomena, serving as a valuable toy model.

Contribution

It provides a detailed analysis of a bosonic gauge theory model with novel features like a non-local Lagrangian, double scaling limits, and a strongly coupled fixed point, expanding understanding of gauge theories with Higgs fields.

Findings

Quantum space of parameters characterized

Non-local Lagrangian for Argyres-Douglas-like CFT derived

Double scaling limit and strong coupling fixed point demonstrated

Abstract

We discuss in details a simple, purely bosonic, quantum field theory belonging to larger class of models with the following properties: a) They are asymptotically free, with a dynamically generated mass scale. b) They have a space of parameters which gets quantum corrections drastically modifying the classical singularity structure. The quantum theory can have massless solitons, Argyres-Douglas-like CFTs, exhibit confinement, etc... c) The physics can, to a large extent, be worked out in models with a large number of supersymmetries as well as in purely bosonic ones. In the former case, exact BPS mass formulas can be derived, brane constructions and embedding in M theory do exist. d) The models have an interesting 1/N expansion, and it is possible to define a double scaling limit in the sense of the ``old'' matrix models when approaching the singularities in parameter space. These properties make these theories very good toy models for four dimensional gauge theories with Higgs fields, and provide a framework where the effects of breaking supersymmetry can be explicitly studied. In our model, we work out in details the quantum space of parameters. We obtain the non-local lagrangian description of the Argyres-Douglas-like CFT, and show that it admits a strongly coupled fixed point. We also explicitly demonstrate property d). The possibility of defining such double scaling limits was not anticipated on the gauge theory side, and could be of interest to understand the gauge theory/string theory correspondence.