Eur. Phys. J. A (2010) 43: 303-311
https://doi.org/10.1140/epja/i2010-10915-1

Regular Article - Theoretical Physics

Comparing topological charge definitions using topology fixing actions

¹ Institut für Theoretische Physik, Universität Regensburg, D-93040, Regensburg, Germany
² Institut für Theoretische Physik III, Universität Erlangen, D-91058, Erlangen, Germany
³ DESY, Platanenallee 6, D-15738, Zeuthen, Germany
⁴ Institut für Physik, Humboldt-Universität zu Berlin, Newtonstraße 15, D-12489, Berlin, Germany
⁵ Faculty of Physics, University of Belgrade, Studentski trg 12, 11000, Belgrade, Serbia

^* e-mail: falk.bruckmann@physik.uni-regensburg.de

Received: 7 July 2009
Revised: 9 December 2009
Accepted: 5 January 2010
Published online: 17 February 2010

Abstract

We investigate both the hyperbolic action and the determinant ratio action designed to fix the topological charge on the lattice. We show to what extent topology is fixed depending on the parameters of these actions, keeping the physical situation fixed. At the same time the agreement between different definitions of topological charge --the field theoretic and the index definition-- is directly correlated to the degree topology is fixed. Moreover, it turns out that the two definitions agree very well. We also study finite-volume effects arising in the static potential and related quantities due to topology fixing.