QCD瞬子与共形时空反演对称性
QCD-Instantons and Conformal Space-Time Inversion Symmetry
摘要：
在本文中，我们探讨了一种吸引人的可能性，即大尺寸QCD瞬子的强抑制-从晶格数据中可以看出-是由于幸存的共形时空反演对称性。这种对称性既来自于在瞬子大小ρ-> ^2 /ρ的反演下瞬子大小分布的高质量晶格数据的惊人不变性<rho>，也来自于经典瞬子扇区中时空反演对称性的已知有效性。在研究共形反演之前，我们通过共形赤平投影将瞬子演算投影到五维球体的四维表面上。这种向紧凑的弯曲几何的投影既是为了避免发散的发生，也是为了从晶格数据中引入平均瞬子尺寸<rho>作为新的长度尺度。平均瞬子大小与这个5d球的半径b相一致，并作为共形反演半径。对于b =<rho>，我们相应的结果是几乎完美对称的时空反演和良好的定性协议与格点数据。当ρ/ b> 0时，我们恢复了平坦四维空间中瞬子微扰理论的熟悉结果。此外，我们说明了（弱破缺）共形反演对称性将有显着的后果QCD超越瞬子。作为反演对称性的进一步成功测试，我们提出了另一个瞬子主导的晶格观察，在QCD真空中的手征翻转比惊人的影响。
英文摘要：
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.
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