Date Thesis Awarded

5-2021

Access Type

Honors Thesis -- Open Access

Degree Name

Bachelors of Science (BS)

Department

Physics

Advisor

Christopher Monahan

Committee Members

Christopher Monahan

Todd Averett

Andreas Stathopoulos

Abstract

Quantum field theory is an extraordinarily successful framework that describes phenomena in particle physics and condensed matter. The O(3) non-linear sigma model (NLSM) is a specific theory used in both of these fields, describing ferromagnets and acting as a prototype for the strong nuclear force. It features topologically stable configurations known as instantons which cannot continuously evolve to the ground state. The topological susceptibility is a parameter that describes this stability and is predicted to vanish in physical theories, however numerical simulations find that the topological susceptibility diverges in the continuum limit. This issue has motivated the application of the “gradient flow”, a smoothing of high-frequency modes. We study the effect of the gradient flow on this divergence, finding that it persists as a logarithmic divergence. This result supports a previous study and indicates that either the definition of topological charge is problematic or the NLSM has no well-defined continuum limit. We also study the nontrivial field theory by introducing a θ-term into the action and analyze the topological charge as a function of θ under the gradient flow.

Recommended Citation

Thomas, Stuart and Monahan, Christopher, "Topology of the O(3) non-linear sigma model under the gradient flow" (2021). Undergraduate Honors Theses. William & Mary. Paper 1621.
https://scholarworks.wm.edu/honorstheses/1621