Novel Approaches to Renormalization Group Transformations in the Continuum and on the Lattice

Abstract

This thesis is about new methods of achieving RG transformations, in both a continuum spacetime background and on a lattice discretization thereof. The subject is explored from the point of view of euclidean quantum field theory. As a thesis grounded on the computational method of lattice simulation, I emphasize the role of lattice formulations throughout the work, especially in the first two chapters. In the first, I describe the essential aspects of lattice theory and its symbiosis with RG. In the second, I present a new, continuous approach to RG on the lattice, based on a numerical tool called Gradient Flow (GF). Simulation results from quartic scalar field theory in 2 and 3 dimensions (${\varphi }_d^4$) and 4-dimensional 12-flavor SU(3) gauge theory will be presented. In the third and fourth chapters, the focus becomes more analytic. Chapter 3 is an introductory review of Functional Renormalization Group (FRG). In chapter 4, I introduce the concept of Stochastic RG (SRG) by working out the relationship between FRG and stochastic processes.

arXiv comment161 pages. PhD thesis, University of Colorado Boulder

References in corpus (18)

• The Exact Renormalisation Group and Approximate Solutions
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• Flavor Symmetry and the Static Potential with Hypercubic Blocking
• Chiral symmetry and the Yang--Mills gradient flow
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• Strongly interacting dynamics and the search for new physics at the LHC
• A Monte Carlo study of leading order scaling corrections of phi^4 theory on a three dimensional lattice
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• Nonperturbative Renormalization of Operators in Near-Conformal Systems Using Gradient Flows
• Finite size scaling of conformal theories in the presence of a near-marginal operator
• Asymptotically safe gravity
• A study of center and chiral symmetry realization in thermal $\mathcal{N}=1$ super Yang-Mills theory using the gradient flow
• Anomalous dimensions on the lattice
• Pion decay constant for the Kogut-Susskind quark action in quenched lattice QCD
• Cooling Stochastic Quantization with colored noise
• Scaling properties of many-fermion systems from MCRG studies
• Renormalisation of the scalar energy-momentum tensor with the Wilson flow