Speaker
Description
The two-dimensional $O(3)$ nonlinear sigma model is a well known toy model for studying non-perturbative phenomena in quantum field theory and QCD. With the latter it shares the fact that there is a non-trivial topological structure and the path integral splits into topological sectors. In the lattice theory topology can be defined as well, but semi-classical arguments suggest that the susceptibility $\chi_t$ does not exhibit the correct continuum scaling. Previously, even when using the gradient flow, this scaling could not be found. We provide results for the dimensionless combination $\chi_t \xi^2$ at large correlation lengths $\xi$ and flowtime $t$ for the standard and tree-level Symanzik improved actions and operators, including a first calculation using the tree-level improved gradient flow. We explicitly quantify finite-volume effects and flow-time discretization errors.