arXivDaily arXiv每日学术速递 周一至周五更新
北美退伍军人节(Veterans Day),12 日无更新
arXiv 0901.2491hep-th
收藏

降维、单极与动力学对称破缺

Dimensional Reduction, Monopoles and Dynamical Symmetry Breaking

Brian P. Dolan, Richard J. Szabo

摘要:

本文研究了M × CP(1)流形上Yang-Mills-Dirac理论的SU(2)-等变降维,重点讨论了非平凡磁通量对CP(1)的影响.杨-米尔斯场的约化给出了M上的一个耦合杨-米尔斯-希格斯系统链,其希格斯势导致动力学对称性破缺,这是杨-米尔斯场的结果。SU(2)对称费米子的约化得到了M上的无质量狄拉克费米子,它在具有汤川耦合的低能规范群下变换,同样是内部U(1)通量的结果。大质量费米子Kaluza-Klein态的塔也有Yukawa相互作用,并且通过用模糊球代替CP(1),允许自然的SU(2)-等变截断。在这种方法中,有可能在具有汤川相互作用的有效场论中获得精确的无质量手征费米子,而没有任何进一步的要求。我们计算出了自发对称性破缺模式,并在一些显式例子中确定了完整的物理粒子谱。

英文摘要:

We consider SU(2)-equivariant dimensional reduction of Yang-Mills-Dirac theory on manifolds of the form M x CP(1), with emphasis on the effects of non-trivial magnetic flux on CP(1). The reduction of Yang-Mills fields gives a chain of coupled Yang-Mills-Higgs systems on M with a Higgs potential leading to dynamical symmetry breaking, as a consequence of the monopole fields. The reduction of SU(2)-symmetric fermions gives massless Dirac fermions on M transforming under the low-energy gauge group with Yukawa couplings, again as a result of the internal U(1) fluxes. The tower of massive fermionic Kaluza-Klein states also has Yukawa interactions and admits a natural SU(2)-equivariant truncation by replacing CP(1) with a fuzzy sphere. In this approach it is possible to obtain exactly massless chiral fermions in the effective field theory with Yukawa interactions, without any further requirements. We work out the spontaneous symmetry breaking patterns and determine the complete physical particle spectrum in a number of explicit examples.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

↑