New Methods and Results for the Topological Susceptibility

Wolfgang Bietenholz (ICN-UNAM)

RESUMEN: In some models of quantum field theory, the configurations are divided into topological sectors. In these models the topological susceptibility is a prominent, non-perturbative observable. We first discuss its definition, and its meaning in QCD and in axion physics. Then we address the difficulty in its numerical measurement. In this regard, we describe a new method ("slab method"), which is applicable even when the Monte Carlo history is confined to a single topological sector. We present results for the quantum rotor, the Heisenberg model and 2-flavor QCD. In the latter case, a modern smoothing procedure is involved, the Gradient Flow. In the second part we focus on the Heisenberg model and the millennium question whether or not its topological susceptibility scales to a finite continuum limit. According to the paradigm of the late 20th century this is not the case, which implies that this famous model suffers from a conceptual disease. However, we are in the process of revisiting this issue by involving for the first time the Gradient Flow also here, along with a powerful cluster algorithm.