arXiv 0903.13992009-03-08hep-thhep-ph

超对称规范理论的降维

Dimensional Reduction of Supersymmetric Gauge Theories

Theodoros Grammatikopoulos

备注：: Ph.D. Thesis (Supervisor: G. Zoupanos), final version published in the Hellenic Dissertations Database of the "National Documentation Centre", 179 pages, 10 tables, 8 figures, uses ltxtable.sty, longtable.sty, xy.sty

摘要：

本论文的主要目的是通过多连通陪集空间上的规范理论的降维，研究四维空间中所有可能的低能模型。高维规范理论被选为杂化弦论所建议的规范理论：（i）它被定义在10维中，（ii）它基于E（8）x E（8）对称群，（iii）它是N=1的全局超对称的。对由上述降维产生的所有四维规范理论的研究，仅限于从唯象观点看可能感兴趣的模型。这一要求限制了这些模型来自于自发对称性破缺的中间阶段的一个已知的大统一理论（GUT）。本文的主要研究结果是，基于Pati-Salam群结构的标准模型可以在四维空间中得到推广。此外，我还回顾了上述思想的一些有趣的非对易推广，并验证了以前的研究工作的一个重要结论，即这种特殊的降维产生的粒子物理模型是可重正化的。最后，假设四维闵可夫斯基空间M^{4}具有非对易特征，我考察了非对易引力的一种特殊方法。事实证明，由于描述空间的代数的非对易结构，里奇曲率张量得到了非平凡的贡献。这一结论表明非对易几何与引力理论之间可能存在根本联系。

英文摘要：

Main objective of the present dissertation is the investigation for all the possible low energy models which emerge in four dimensions by the dimensional reduction of a gauge theory over multiple connected coset spaces. The higher dimensional gauge theory is chosen to be the one that the Heterotic string theory suggests: (i) it is defined in ten dimensions, (ii) it is based on the E(8) x E(8) symmetry group and (iii) it is N=1 globally supersymmetric. The search of all four-dimensional gauge theories resulting from the aforementioned dimensional reduction, is restricted only to models which are potentially interesting from a phenomenological point of view. This requirement constrain these models to come from one of the known Grand Unified Theories (GUTs) in an intermediate stage of the spontaneous symmetry breaking. Main result of my study is that extensions of the Standard Model (SM) which are based on the Pati-Salam group structure can be obtained in four dimensions. I furthermore review some interesting noncommutative generalizations of the above ideas and verify an important conclusion of a previous research work, namely that the particle physics models resulting from this particular dimensional reduction are renormalizable. Finally, assuming noncommutative characteristics for the four-dimensional Minkowski space, M^{4}, I examine a particular approach of noncommutative gravity. It turns out that the Ricci curvature tensor receives non-trivial contributions due to the noncommutative structure of the algebra describing the space, This conclusion suggests a possible fundamental connection between the noncommutative geometry and the theory of gravity.

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英文摘要：

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