Perfect topological charge for asymptotically free theories

M. Blatter; R. Burkhalter; P. Hasenfratz; F. Niedermayer

doi:10.1016/0920-5632(95)00385-M

paper

Perfect topological charge for asymptotically free theories

arXiv:hep-lat/9411068 · doi:10.1016/0920-5632(95)00385-M

Abstract

The classical equations of motion of the perfect lattice action in asymptotically free $d = 2$ spin and $d = 4$ gauge models possess scale invariant instanton solutions. This property allows the definition of a topological charge on the lattice which is perfect in the sense that no topological defects exist. The basic construction is illustrated in the $d = 2$ O(3) non--linear $σ$ --model and the topological susceptibility is measured to high precision in the range of correlation lengths $ξ \in (2 - 60)$ . Our results strongly suggest that the topological susceptibility is not a physical quantity in this model.

Contribution to Lattice'94, 3 pages PostScript, uuencoded compressed