QCD-Instantons and Conformal Space-Time Inversion Symmetry

TL;DR

This paper investigates the hypothesis that conformal space-time inversion symmetry explains the suppression of large-size QCD instantons, using conformal mapping and lattice data to support the symmetry's role in instanton physics.

Contribution

It introduces a conformal stereographic projection approach to analyze instantons, revealing near-symmetry under space-time inversion and connecting lattice data with theoretical symmetry considerations.

Findings

Invariance of instanton size distribution under inversion observed in lattice data.

Conformal inversion symmetry nearly holds when average instanton size matches the sphere radius.

Implications for QCD observables like the chirality-flip ratio support the symmetry's relevance.

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 rho --> <rho>^2 / rho 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 <rho> 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 = <rho>, our corresponding results are almost perfectly symmetric under space-time inversion and in good qualitative agreement with the lattice data. For rho / 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.