Lattice determination of the topological susceptibility slope $\chi^\prime$ of $2d~\mathrm{CP}^{N-1}$ models at large $N$

TL;DR

This paper calculates the topological susceptibility slope in 2D CP^{N-1} models using lattice Monte Carlo simulations for various N, employing a double limit approach to improve understanding of topological properties relevant to higher-dimensional theories.

Contribution

It introduces a double limit strategy for computing the topological susceptibility slope on the lattice, applicable to 2D models and potentially extendable to 4D gauge theories and QCD.

Findings

Successfully computed $ heta'$ for N=5,11,21,31

Established a double limit procedure for lattice calculations

Provides a foundation for future studies in 4D gauge theories

Abstract

We compute the topological susceptibility slope $\chi^\prime$, related to the second moment of the two-point correlator of the topological charge density, of $2d$ $\mathrm{CP}^{N-1}$ models for $N=5,11,21$ and $31$ from lattice Monte Carlo simulations. Our strategy consists in performing a double limit: first, we take the continuum limit of $\chi^\prime$ at fixed smoothing radius in physical units; then, we take the zero-smoothing-radius limit. Since the same strategy can also be applied to $4d$ gauge theories and full QCD, where $\chi^\prime$ plays an intriguing theoretical and phenomenological role, this work constitutes a step towards the lattice investigation of this quantity in such models.