Lattice determination of the topological susceptibility slope <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msup><mml:mi>χ</mml:mi><mml:mo>′</mml:mo></mml:msup></mml:math> of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>2</mml:mn><mml:mi>d</mml:mi></mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>CP</mml:mi></mml:mrow><mml:mrow><mml:mi>N</mml:mi><mml:mo>−</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:msup></mml:mrow></mml:math> models at large <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>N</mml:mi></mml:math>
Claudio Bonanno
Abstract
We compute the topological susceptibility slope ${\ensuremath{\chi}}^{\ensuremath{'}}$, related to the second moment of the two-point correlator of the topological charge density, of $2d$ ${\mathrm{CP}}^{N\ensuremath{-}1}$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}$ 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 ${\ensuremath{\chi}}^{\ensuremath{'}}$ plays an intriguing theoretical and phenomenological role, this work constitutes a step toward the lattice investigation of this quantity in such models.