The Topological Susceptibility of the Lattice CP(n-1) Model on the Torus and the Sphere

TL;DR

This paper investigates the topological susceptibility of the lattice CP(n-1) model on different geometries, revealing unexpected deviations at higher n and potential convergence to large-n analytical results.

Contribution

It provides the first lattice study of the topological susceptibility of the CP(n-1) model on both torus and sphere geometries, comparing results with continuum and large-n predictions.

Findings

Topological susceptibility deviates from asymptotic scaling for n ≥ 5.

Evidence suggests convergence to large-n analytical values.

Differences observed between torus and sphere geometries.

Abstract

The topological vacuum structure of the two-dimensional $~CP^{n-1}~$ model for $~n = 3,5,7~$ is studied on the lattice. In particular we investigate the small-volume limit on the torus as well as on the sphere and compare with continuum results. For $~n \ge 5~$ , where lattice artifacts should be suppressed, the topological susceptibility shows unexpectedly strong deviations from asymptotic scaling. On the other hand there is an indication for a convergence to values obtained analytically within the limit $~n \rightarrow \infty~$ .