arXiv 1002.26062010-02hep-thhep-ph

Orbifolds，fuzzy sphere和手征费米子

Orbifolds, fuzzy spheres and chiral fermions

Athanasios Chatzistavrakidis, Harold Steinacker, George Zoupanos

备注：: 24 pages, minor changes, references added, matching with the published version
发表信息：: JHEP 1005:100,2010
DOI：: 10.1007/JHEP05(2010)100

摘要：

我们从一个N=4的四维超对称杨-米尔斯理论出发，用规范群SU（3 N）进行轨道投影，得到一个N=1的超对称SU（N）^3杨-米尔斯理论，它的物质超多重态是规范群的双基本表象，是手征的、无反常的。随后，我们寻找真空的投影理论，可以解释为自发产生的扭曲模糊球。我们表明，通过添加适当的软超对称性破缺项，我们确实可以揭示这样的真空。研究了三种情况，其中规范群自发进一步破缺为低能规范群SU（4）xSU（2）xSU（2）、SU（4）^3和SU（3）^3。这种模型在中间尺度下表现为具有有限卡鲁扎-克莱因塔的高维理论，而它们的低能物理由相应的零模控制，并在费米扇区中表现出手征性。从唯象学的观点来看，最有趣的情况是SU（3）^3统一理论，它有几个有趣的特征，例如（i）它可以被提升为有限理论，（ii）由于它自己的标量扇区，它首先自发地进一步分裂为MSSM，然后分裂为SU（3）xU（1）_{em}，即不需要额外的超场，以及（iii）相应的真空导致自发产生的模糊球。

英文摘要：

Starting with a N=4 supersymmetric Yang-Mills theory in four dimensions with gauge group SU(3N) we perform an orbifold projection leading to a N=1 supersymmetric SU(N)^3 Yang-Mills theory with matter supermultiplets in bifundamental representations of the gauge group, which is chiral and anomaly free. Subsequently, we search for vacua of the projected theory which can be interpreted as spontaneously generated twisted fuzzy spheres. We show that by adding the appropriate soft supersymmetry breaking terms we can indeed reveal such vacua. Three cases are studied, where the gauge group is spontaneously broken further to the low-energy gauge groups SU(4)xSU(2)xSU(2), SU(4)^3 and SU(3)^3. Such models behave in intermediate scales as higher-dimensional theories with a finite Kaluza-Klein tower, while their low-energy physics is governed by the corresponding zero-modes and exhibit chirality in the fermionic sector. The most interesting case from the phenomenological point of view turns out to be the SU(3)^3 unified theory, which has several interesting features such as (i) it can be promoted to a finite theory, (ii) it breaks further spontaneously first to the MSSM and then to SU(3)xU(1)_{em} due to its own scalar sector, i.e. without the need of additional superfields and (iii) the corresponding vacua lead to spontaneously generated fuzzy spheres.

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