Precision study of the SU(3) topological susceptibility in the continuum

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 definitio...

We find that using open boundary condition in the temporal direction can yield the expected value of the topological susceptibility in lattice SU(3) Yang-Mills theory. As a further check, we show that the result agrees with numerical simulations employing the periodic boundary condition. Our results support the preferability of the open boundary condition over the periodic boundary condition as the former allows for computation at smaller lattice spacings needed for continuum...

We investigate the topological properties of the $SU(3)$ pure gauge theory by performing numerical simulations at imaginary values of the $\theta$ parameter. By monitoring the dependence of various cumulants of the topological charge distribution on the imaginary part of $\theta$ and exploiting analytic continuation, we determine the free energy density up to the sixth order order in $\theta$, $f(\theta,T) = f(0,T) + {1\over 2} \chi(T) \theta^2 (1 + b_2(T) \theta^2 + b_4(T) \...

We study on the lattice the topology of SU(2) and SU(3) Yang-Mills theories at zero temperature and of QCD at temperatures around the phase transition. To smooth out dislocations and the UV noise we cool the configurations with an action which has scale invariant instanton solutions for instanton size above about 2.3 lattice spacings. The corresponding "improved" topological charge stabilizes at an integer value after few cooling sweeps. At zero temperature the susceptibility...

We compute the topological susceptibility of the SU(N) Yang-Mills theory in the large-N limit with a percent level accuracy. This is achieved by measuring the gradient-flow definition of the susceptibility at three values of the lattice spacing for N=3,4,5,6. Thanks to this coverage of parameter space, we can extrapolate the results to the large-N and continuum limits with confidence. Open boundary conditions are instrumental to make simulations feasible on the finer lattices...

In this paper we investigate, by means of numerical lattice simulations, the topological properties of the trace deformed $SU(3)$ Yang-Mills theory defined on $S_1\times\mathbb{R}^3$. More precisely, we evaluate the topological susceptibility and the $b_2$ coefficient (related to the fourth cumulant of the topological charge distribution) of this theory for different values of the lattice spacing and of the compactification radius. In all the cases we find results in good agr...

We present a scheme for the analytic computation of renormalization functions on the lattice, using a symbolic manipulation computer language. Our first nontrivial application is a new three-loop result for the topological susceptibility.

Memorizing Pierre van Baal we will shortly review his life and his scientific achievements. Starting then with some basics in gauge field topology we mainly will discuss recent efforts in determining the topological susceptibility in lattice QCD.

SU(2) gauge theory is investigated with a lattice action which is insensitive to small perturbations of the lattice gauge fields. Bare perturbation theory can not be defined for such actions at all. We compare non-perturbative continuum results with that obtained by the usual Wilson plaquette action. The compared observables span a wide range of interesting phenomena: zero temperature large volume behavior (topological susceptibility), finite temperature phase transition (cri...

We present some new three-loop results in lattice gauge theories, for the Free Energy and for the Topological Susceptibility. These results are an outcome of a scheme which we are developing (using a symbolic manipulation language), for the analytic computation of renormalization functions on the lattice.