Studies with Improved Renormalization Group Techniques
The discovery of the Higgs Boson at the Large Hadron Collider in 2012 completes the Electroweak Sector of the Standard Model. Although the Standard Model is complete with a scalar Higgs, the hierarchy problem raises concerns about a scalar mechanism for electroweak symmetry breaking. Strongly interacting gauge-fermion systems that break electroweak symmetry are an interesting alternative because they provide an ultraviolet completion to the Standard Model. The only reliable technique to study strongly interacting quantum field theories is a numerical technique called Lattice Gauge Theory.
In this dissertation I describe lattice studies of SU(3) gauge theories with many flavors of chiral fermions in the fundamental representation. This is part of a larger effort to find a viable composite Higgs model. I employ lattice renormalization group techniques to study the infrared properties of these theories. Additionally I show how it is possible to improve traditional techniques with an optimization step. Results indicate that SU(3) 12 flavors is a conformal field theory while the 8 flavor theory is confining and spontaneously breaks chiral symmetry.