Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories

TL;DR

This dissertation investigates conformal and nearly conformal quantum field theories nonperturbatively, focusing on lattice studies of SU(3) gauge theory with eight flavors, and develops effective field theories to understand their low-energy behavior.

Contribution

It introduces a new EFT framework based on the linear sigma model for nearly conformal gauge theories and provides lattice results for scattering processes to constrain these theories.

Findings

Identification of the light flavor-singlet scalar as a potential composite Higgs.

New lattice data for $mbda$ scattering using L"uscher's method.

Proposal of an EFT approach combining lattice and analytical techniques.

Abstract

In this dissertation, we present work towards characterizing various conformal and nearly conformal quantum field theories nonperturbatively using a combination of numerical and analytical techniques. A key area of interest is the conformal window of four dimensional gauge theories with Dirac fermions and its potential applicability to beyond the standard model physics. In the first chapter, we review some of the history of models of composite Higgs scenarios in order to motivate the study of gauge theories near the conformal window. In the second chapter we review lattice studies of a specific theory, SU(3) gauge theory with eight flavors of Dirac fermions in the fundamental representation of the gauge group. We place a particular emphasis on the light flavor-singlet scalar state appearing in the spectrum of this model and its possible role as a composite Higgs boson. We advocate an approach to characterizing nearly conformal gauge theories in which lattice calculations are used to identify the best low energy effective field theory (EFT) description of such nearly conformal gauge theories, and the lattice and EFT are then used as complementary tools to classify the generic features of the low energy physics in these theories. We present new results for maximal isospin $\pi\pi \rightarrow \pi\pi$ scattering on the lattice computed using L\"uscher's finite volume method. This scattering study is intended to provide further data for constraining the possible EFT descriptions of nearly conformal gauge theory. In Chapter 3, we review the historical development of chiral effective theory from current algebra methods up through the chiral Lagrangian and modern effective field theory techniques. We present a new EFT framework based on the linear sigma model for describing the low lying states of nearly conformal gauge theories. We place a ... (full abstract within)