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

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.

Comments: 10 pages, 19 eps figures; v2: few typos corrected, matches published version