Testing the WittenVeneziano mechanism with the YangMills gradient flow on the lattice
Abstract
We present a precise computation of the topological charge distribution in the $SU(3)$ YangMills 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 YangMills gradient flow. The flow equations are integrated numerically by a fourthorder structurepreserving RungeKutta 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.
 Publication:

arXiv eprints
 Pub Date:
 October 2014
 arXiv:
 arXiv:1410.8358
 Bibcode:
 2014arXiv1410.8358C
 Keywords:

 High Energy Physics  Lattice;
 High Energy Physics  Theory
 EPrint:
 7 pages, 6 figures, talk presented at the 32nd International Symposium on Lattice Field Theory  Lattice 2014, June 2328, 2014, Columbia University New York, NY