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arXiv 1811.04428hep-thmath-phmath.MP
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四维共形场论中的强子扇形

Hadronic Sector in the 4-d Pseudo-Conformal Field Theory

C. N. Ragiadakos

备注：
arXiv admin note: text overlap with arXiv:1805.11966
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摘要：

伪共形场论（PCFT）是一种四维作用量，它依赖于洛仑兹柯西-黎曼（LCR）结构。像二维线性化弦作用量一样，它不依赖于度规张量。但在伪共形变换下的不变性使作用量中存在规范场，而不是弦作用量的标量场。LCR-结构的四元组定义了一类度量和相应的一类自对偶2-形式。从孤子和多孤子的角度描述了光子晶体光纤传输，并与爱因斯坦运动方程的推导有关。在静态LCR结构孤子周围的作用量展开后，类Yang-Mills项的二次部分隐含一个线性偏微分方程（PDE）。我解决这个偏微分方程使用Teukolsky方法的解决方案的电磁场的背景下的克尔黑洞。角向和径向常微分方程与相应的Teukolsky主方程不同。利用LCR-结构坐标的基本性质，求解了精确的规范场偏微分方程。所发现的解具有有色的源，可以用夸克来识别。

英文摘要：

The pseudo-conformal field theory (PCFT) is a 4-d action, which depends on the lorentzian Cauchy-Riemann (LCR) structure. Like the 2-d linearized string action, it does not depend on the metric tensor. But the invariance under the pseudo-conformal transformations imposes in the action the existence of a gauge field instead of the scalar field of the string action. The tetrad of the LCR-structure defines a class of metrics and a corresponding class of self dual 2-forms. Soliton and multisoliton point of view of PCFT is described and related to the Einstein derivation of the equations of motion. After the expansion of the action around the static LCR-structure soliton, the quadratic part of the Yang-Mills-like term implies a linear partial differential equation (PDE). I solve this PDE using the Teukolsky method for the solution of the electromagnetic field in the background of the Kerr black hole. The angular and radial ODEs are different from the corresponding Teukolsky master equations. The exact gauge field PDEs are also solved, solved, using the fundamental property of LCR-structure coordinates. The found solutions have colored sources, which could be identified with the quarks.

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