Topological susceptibility in the Yang-Mills theory in the vacuum correlator method

Abstract

We calculate the topological susceptibility of the Yang-Mills vacuum using the field correlator method. Our estimate for the SU (3) gauge group, χ 1/4 = 196(7) MeV, is in a very good agreement with the results of recent numerical simulations of the Yang-Mills theory on the lattice.

Topological density fluctuations and gluon condensate around confining string in Yang–Mills theory

“…Indeed, the topological susceptibility -given by a volume integral of the two-point correlator of topological densities -can be calculated both on the lattice with the use of numerical methods and in the continuum limit, analytically. In the latter case the field correlator technique can be applied in rather straightforward manner [16]. The analytical and numerical results coincide with each other.…”

“…Our next step is to evaluate the correlation function (8) in the field correlator approach. Using the factorization of the correlator of the four field strengths operators [16], we get for the N = 2 case:…”

“…which was evaluated in with the help of the field correlator method in Ref. [16]. In this paper we are interested in local fluctuations of the topological charge, which are given by the local susceptibility…”

“…Here we used the subscript "q" in order to discriminate the local susceptibility (17) from the standard global one (16), χ Q . In order to probe the distribution of the local fluctuations of the topological charge around the string one needs at least four plaquette probes.…”

θ dependence of SU(N) gauge theories in the presence of a topological term

“…(2.13) and (2.15); the difference between the estimates is of course related to the uncertainty in the physical scale for σ and for r 0 . We also mention that the topological susceptibility of a pure SU (3) gauge theory has been also studied by QCD spectral sum rule methods [419][420][421], leading to the estimate χ 1/4 ≈ 120 MeV, and by the fieldcorrelator method [138] 6.2 The topological susceptibility for N > 3 and in the large-N limit…”