Topological Susceptibility under Gradient Flow

¹ Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México A.P. 70-543, C.P. 04510 Ciudad de México, Mexico
² Goethe-Universität Frankfurt am Main, Institut für Theoretische Physik Max-von-Laue-Straße 1, 60438 Frankfurt am Main, Germany
³ Faculty of Physics, Adam Mickiewicz University, Umultowska 85, 61-614 Poznán, Poland
⁴ Institut für Theoretische Physik, ETH Zürich, Wolfgang-Pauli-Strasse 27, CH–8093 Zürich, Switzerland
⁵ CERN, Theory Division, CH-1211 Genève 23, Switzerland
⁶ Institut für Theoretische Physik, Universität Regensburg, D-93040 Regensburg, Germany
⁷ Instituto de Física y Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo Edificio C-3, Apdo. Postal 2-82, C.P. 58040, Morelia, Michoacán, Mexico

^* Speaker, e-mail: he_mejia@yahoo.com.mx

Published online: 26 March 2018

Abstract

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility X_t is measured directly, and by the slab method, which is based on the topological content of sub-volumes (“slabs”) and estimates X_t even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, ξ²). This ongoing study is based on direct measurements of X_t in L × L lattices, at L/ξ ≃6.