The 38th International Symposium on Lattice Field Theory

D2: Topology of the $O(3)$ non-linear sigma model under the gradient flow

28 Jul 2021, 15:00

1h

Poster Theoretical developments and applications beyond particle physics Poster

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.

Presentation materials

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