### Speaker

Stuart Thomas
(William & Mary)

### Description

The $O(3)$ non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, featuring topological qualities. Though the topological susceptibility $\chi_t$ should vanish in physical theories, lattice simulations of the NLSM find that $\chi_t$ diverges in the continuum limit. We study the effect of the gradient flow on this quantity using a Markov chain Monte Carlo method, finding that a logarithmic divergence persists. 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 introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow.

### Primary authors

Stuart Thomas
(William & Mary)
Christopher Monahan
(William & Mary)