The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory

TL;DR

This paper accurately computes the topological susceptibility of SU(N) Yang-Mills theory in the large N limit using lattice simulations with improved techniques, confirming large N scaling with high precision.

Contribution

It introduces advanced lattice methods, including gradient flow and open boundary conditions, enabling precise large N extrapolation of topological susceptibility.

Findings

Successful continuum and large N extrapolation of $ imes_0^2\,\chi_{YM}$

Enhanced lattice techniques improve accuracy of topological measurements

Verification of large N scaling with unprecedented precision

Abstract

We present a precise computation of the topological susceptibility $\chi_{_\mathrm{YM}}$ of SU$(N)$ Yang-Mills theory in the large $N$ limit. The computation is done on the lattice, using high-statistics Monte Carlo simulations with $N=3, 4, 5, 6$ and three different lattice spacings. Two major improvements make it possible to go to finer lattice spacing and larger $N$ compared to previous works. First, the topological charge is implemented through the gradient flow definition; and second, open boundary conditions in the time direction are employed in order to avoid the freezing of the topological charge. The results allow us to extrapolate the dimensionless quantity $t_0^2\chi_{_\mathrm{YM}}$ to the continuum and large $N$ limits with confidence. The accuracy of the final result represents a new quality in the verification of large $N$ scaling.