Andrew Gasbarro

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 application to BSM model building.

We advocate a research program in which the generic low energy physics of nearly-conformal gauge theories is characterized by combining lattice computations of specific gauge theories with more general effective field theory (EFT) analyses. We review lattice studies of the spectrum of a particular nearly-conformal gauge theory, eight flavor QCD, and discuss the light flavor-singlet scalar state as a candidate for a composite Higgs boson. New lattice results are presented for the maximal isospin pi-pi scattering length in the eight-flavor model. We compare the scattering length in the eight-flavor model to the scattering length in two- and six-flavor QCD and to the prediction from leading order chiral perturbation theory. Next, we present a new EFT framework based on the linear sigma model for describing the low-lying states of nearly conformal gauge theories. A particular emphasis is placed on the chiral breaking potential and the power counting of the spurion field. Explicit fits of the model to lattice data are shown.

In the second half of the talk, we report on a new formulation of lattice quantum field theory suited for studying conformal field theories (CFTs) nonperturbatively in radial quantization. We demonstrate that this method is not only applicable to CFTs, but more generally for formulating a lattice regularization of quantum field theory on an arbitrary smooth Riemann manifold. The general procedure, which we refer to as quantum finite elements (QFE), is reviewed for scalar fields. Explicit numerical studies are presented for scalar phi-4 theory on the 2-sphere. We demonstrate that it is in close statistical agreement with the c=1/2 minimal 2D Ising CFT. We also investigate scalar phi-4 theory on R X S^2, and we report on progress towards studying the 3D Ising CFT in radial quantization on the lattice. Future directions for the method are discussed.