Effects of topological charge in asymptotically free gauge theories.

摘要

In this thesis I report the results of a study of the effects of topological charge in the CPN-1 models and QCD. In QCD topological charge is responsible for the mass of the eta' particle, and is closely connected to chiral symmetry breaking, while in CP N-1 the details of the distribution of topological charge affect the behavior of the vacuum free energy and the nature of confinement.;In the two-dimensional CPN-1 model a fractionally charged Wilson loop creates a 6-vacuum in the region of spacetime lying within the loop. I describe how we implemented fractionally charged Wilson loops on the lattice and present measurements of the free energy density epsilon(theta). Our lattice results show that the CP1 free energy is in good quantitative agreement with the dilute instanton gas approximation. The CP5 and CP9 models display a cusp at theta = pi which supports the large N argument for discrete, degenerate vacua.;The second part of the thesis describes preliminary results of an investigation of topological charge in the three-dimensional CP 1 model. We discuss the monopole structure of topological charge and present preliminary Monte Carlo results for gauge configurations with monopole suppression. Our results suggest that gauge configurations with no monopoles may be organized into a discrete set of distinct topological sectors based upon the net number of closed magnetic flux loops that wrap around the entire lattice (periodic flux loops) in each of the three spacetime directions. We argue that a proper description of the vacuum state should include contributions from all of the topological sectors, and that regions of the phase diagram that include periodic flux loops should exhibit confinement of the zi particles.;In the final chapter of the thesis I describe a calculation we performed to test a proposed equivalence between N = 1 Supersymmetric Yang-Mills theory and ordinary 1-flavor QCD. This calculation clarifies the important role of QCD topological charge in the dynamics of this equivalence. We also study the role of q q annihilation in the 1- and 2-flavor Nambu-Jonc Lasinio model, where annihilation terms arise from the chiral field determinant representing the axial U(1) anomaly.