Studies of Conformal Behavior in Strongly Interacting Quantum Field Theories

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 $\pi \pi \to \pi \pi$ scattering on the lattice computed using Lüscher'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)

Ph.D. Thesis, Yale University 2018, 154 Pages

References in corpus (15)

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• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Isoscalar $\pi \pi$ scattering and the $\sigma$ meson resonance from QCD
• The infrared dynamics of Minimal Walking Technicolor
• Lattice simulations with eight flavors of domain wall fermions in SU(3) gauge theory
• Fate of the conformal fixed point with twelve massless fermions and SU(3) gauge group
• Nonperturbative beta function of eight-flavor SU(3) gauge theory
• Lattice QCD study of the s-wave $\pi \pi$ scattering lengths in the I=0 and 2 channels
• Meson-meson Scattering in QCD-like Theories
• Parity Doubling and the S Parameter Below the Conformal Window
• S-parameter and pseudo-Nambu-Goldstone boson mass from lattice QCD
• A Chiral Perturbation Theory Primer
• Strong dynamics, composite Higgs and the conformal window
• A linear sigma model for multiflavor gauge theories
• Improved Lattice Radial Quantization