QCD-Instantons and Conformal Space-Time Inversion Symmetry

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 highquality 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.