QCD-Instantons and conformal space-time inversion symmetry

Abstract

F. SchremppDeutsches Elektronen-Synchrotron DESY, Hamburg, Germany E-mail: fridger.schrempp@desy.de Abstract: In this paper, we explore the appealing possibility that the strong suppression of large-size QCD instantons -as evident from lattice data -is due to a surviving conformal space-time inversion symmetry. This symmetry is both suggested from the striking invariance of high-quality lattice data for the instanton size distribution under inversion of the instanton size ρ → ρ 2 /ρ and from the known validity of space-time inversion symmetry in the classical instanton sector. We project the instanton calculus onto the four-dimensional surface of a five-dimensional sphere via conformal stereographic mapping, before investigating conformal inversion. This projection to a compact, curved geometry is both to avoid the occurence of divergences and to introduce the average instanton size ρ from the lattice data as a new length scale. The average instanton size is identified with the radius b of this 5d-sphere and acts as the conformal inversion radius. For b = ρ , our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For ρ/b → 0 we recover the familiar results of instanton perturbation theory in flat 4d-space. Moreover, we illustrate that a (weakly broken) conformal inversion symmetry would have significant consequences for QCD beyond instantons. As a further successful test for inversion symmetry, we present striking implications for another instanton dominated lattice observable, the chirality-flip ratio in the QCD vacuum.

Gaussian sum rules for 0−+glueball in the instanton vacuum model

“…In fact, the condensate contributions turned out to be very small as compared with those of instantons in the glueball channels and may be understood as a small fraction of the corresponding instanton one in the local limit. Furthermore, as discussed in [7], the topological charge screening effect of the pseudoscalar current and the role of the instanton size distribution [7,20,[25][26][27][28] (also see [29,30] for recent researches) are taken into account in order to improve our sum rule results.…”