Testing the Witten-Veneziano mechanism with the Yang-Mills gradient flow on the lattice

We present a precise computation of the topological charge distribution in the \(SU(3)\) Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. Th...

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Bibliographic Details
Published in:arXiv.org 2014-10
Main Authors: Cè, Marco, Consonni, Cristian, Engel, Georg P, Giusti, Leonardo
Format: Article
Language:English
Subjects:
Charge distribution
Computer simulation
Confidence
Field strength
Flow equations
Gradient flow
Mathematical models
Monte Carlo simulation
Runge-Kutta method
Systematic errors
Tensors
Topology
Yang-Mills theory
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Summary:We present a precise computation of the topological charge distribution in the \(SU(3)\) Yang-Mills theory. It is carried out on the lattice with high statistics Monte Carlo simulations by employing the clover discretization of the field strength tensor combined with the Yang-Mills gradient flow. The flow equations are integrated numerically by a fourth-order structure-preserving Runge-Kutta method. We have performed simulations at four lattice spacings and several lattice sizes to remove with confidence the systematic errors in the second (topological susceptibility \(\chi_t^\text{YM}\)) and the fourth cumulant of the distribution. In the continuum we obtain the preliminary results \(t_0^2\chi_t^\text{YM}=6.53(8)\times 10^{-4}\) and the ratio between the fourth and the second cumulant \(R=0.233(45)\). Our results disfavour the \(\theta\)-behaviour of the vacuum energy predicted by dilute instanton models, while they are compatible with the expectation from the large-\(N_c\) expansion.
ISSN:2331-8422