Topological susceptibility and string tension in the lattice CP(N) models

TL;DR

This paper investigates topological susceptibility and string tension in lattice CP(N) models through numerical simulations at N=4 and N=10, testing universality and scaling, and examining confinement without screening effects.

Contribution

It provides a comparative analysis of different lattice formulations for topological susceptibility and confirms confinement in CP(N) models at large N without screening.

Findings

Geometrical approach yields reliable topological susceptibility at N=10.

Unphysical dislocations affect susceptibility measurements at N=4.

String tension indicates confinement without screening effects.

Abstract

In the lattice CP(N) models we studied the problems related to the measure of the topological susceptibility and the string tension . We perfomed numerical simulations at N=4 and N=10. In order to test the universality, we adopted two different lattice formulations. Scaling and universality tests led to the conclusion that at N=10 the geometrical approach gives a good definition of lattice topological susceptibility. On the other hand, N=4 proved not to be large enough to suppress the unphysical configurations, called dislocations, contributing to the topological susceptibility. We obtained other determinations of the topological susceptibility by the field theoretical method, wich relies on a local definition of the lattice topological charge density, and the cooling method. They gave quite consistent results, showing scaling and universality. The large-N expansion predicts an exponential area law behavior for sufficiently large Wilson loops, which implies confinement, due to the dynamical matter fields and absence of the screening phenomenon. We determined the string tension, without finding evidence of screening effects.