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

Abstract

The O(3) non-linear sigma model (NLSM) is a prototypical field theory for QCD and ferromagnetism, and provides a simple system in which to study topological effects. In lattice QCD, the gradient flow has been demonstrated to remove ultraviolet singularities from the topological susceptibility. In contrast, lattice simulations of the NLSM find that the topological susceptibility diverges in the continuum limit, even in the presence of the gradient flow. We introduce a $\theta$-term and analyze the topological charge as a function of $\theta$ under the gradient flow. Our results show that divergence persists in the presence of the flow, even at non-zero $\theta$.

The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

References in corpus (6)

• Infinite N phase transitions in continuum Wilson loop operators
• Locally smeared operator product expansions in scalar field theory
• Renormalizability of the gradient flow in the 2D $O(N)$ non-linear sigma model
• Generalized Gradient Flow Equation and Its Application to Super Yang-Mills Theory
• $\theta$-dependence in the small-$N$ limit of $2d$ $C{P}^{N-1}$ models
• Numerical study of the mass spectrum in the 2D O(3) sigma model with a theta term