Gauge invariant field strength correlators from RG smoothing and color correlations between topological charge clusters

Abstract

Using the renormalization group based smoothing technique we have studied the gauge invariant field strength correlator at T = 0 and T = 0 in pure SU (2) gauge theory. In conjunction with a cluster analysis, the field strength correlator is used to study correlations between the clusters in space and color orientation.

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

“…Similar results were obtained in Ref. [9] with the use of the so called renormalization group smoothing which is an alternative to the cooling.…”

“…In what follows we consider the quadratic correlator (9) for which various numerical estimations are available [7,8,9]. The numerical results were obtained in lattice simulations with the use of the so-called cooling method which makes it possible to get rid of short-range lattice artifacts while leaving the long-range physics intact.…”

“…Another subtlety of the lattice results is the dependence of the correlators on the shape of the Schwinger line connecting the points x 0 , x 1 and x 2 in the definition of the correlator (9). It turns out that the dependence of the prefactors A i and b i , i = 0, 1 is rather strong, while the correlation lengths T g and λ are insensitive with respect to the variations of the shape of the line [10].…”

“…It turns out that the dependence of the prefactors A i and b i , i = 0, 1 is rather strong, while the correlation lengths T g and λ are insensitive with respect to the variations of the shape of the line [10]. Thus our results should be understood with the prescription that the perturbative ultraviolet corrections are subtracted and the Schwinger line itself is chosen to take a most natural shape forming straight path stretched between the points x and x 2 in the definition of the correlation function (9). In this prescription the correlator is clearly independent of the reference point x 0 provided it is located on the Schwinger line stretched between the points x 1 and x 2 .…”

“…In this calculation we identified the field strength tensors F µν -used in the definition of the topological charge density (4) -with the covariantly transformed field strength tensors G µν , Eq. ( 6), used in the definition of the gauge-invariant bilocal correlators (9). We used the observation that the four-point correlation function (13) involves only two distinct points x 1 = 0 and x 2 = z.…”