PoS - Proceedings of Science
Volume 256 - 34th annual International Symposium on Lattice Field Theory (LATTICE2016) - Vacuum Structure and Confinement
The large $N$ limit of the topological susceptibility of Yang-Mills gauge theory
M. Cè, M.F. Garcia Vera,* L. Giusti, S. Schaefer
*corresponding author
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Pre-published on: February 16, 2017
Published on: March 24, 2017
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.
DOI: https://doi.org/10.22323/1.256.0350
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