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

We compute the topological susceptibility slope ${\chi }^{\mathrm{\prime }}$, related to the second moment of the two-point correlator of the topological charge density, of $2d$ ${\mathrm{C}\mathrm{P}}^{N-1}$ 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 ${\chi }^{\mathrm{\prime }}$ 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 ${\chi }^{\mathrm{\prime }}$ plays an intriguing theoretical and phenomenological role, this work constitutes a step towards the lattice investigation of this quantity in such models.