Asymptotically free four-Fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
Asymptotically free four-Fermi theory in 4 dimensions at the z=3 Lifshitz-like fixed point
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z=3 Lifshitz 类不动点处 4 维渐近自由四费米理论
DOI：
10.1103/physrevd.80.105018
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发表时间：
2009
影响因子：
5
通讯作者：
S. Wadia
中科院分区：
文献类型：
--
作者：
A. Dhar;G. Mandal;S. Wadia
我们证明了3+1维空间中在z=3 Lifshitz型不动点处的Nambu-Jona-Lasinio型四费米子耦合是渐近自由的，并动态地产生一个质量标度.这一结果在费米子种类较多的情况下是非微扰的。这个理论是紫外线完全的，并且在低能量下表现出洛伦兹不变性作为一个涌现的时空对称性。我们的许多结果推广到z=d在奇数d空间维度; z=d=1对应于Gross-Neveu模型。上述质量产生机制对费米子质量问题和动力学电弱对称性破缺有潜在的应用。我们提出了一个方案，其中复合希格斯场产生于这些费米子的凝聚，然后耦合到夸克和轻子的标准模型。这样的情况可以消除对希格斯势和相关层次问题的需要。我们还表明，在z=3的轴向异常公式符合通常的相对论域。
We show that a Nambu-Jona-Lasinio type four-fermion coupling at the z=3 Lifshitz-like fixed point in 3+1 dimensions is asymptotically free and generates a mass scale dynamically. This result is nonperturbative in the limit of a large number of fermion species. The theory is ultraviolet complete and at low energies exhibits Lorentz invariance as an emergent spacetime symmetry. Many of our results generalize to z=d in odd d spatial dimensions; z=d=1 corresponds to the Gross-Neveu model. The above mechanism of mass generation has potential applications to the fermion mass problem and to dynamical electroweak symmetry breaking. We present a scenario in which a composite Higgs field arises from a condensate of these fermions, which then couples to quarks and leptons of the standard model. Such a scenario could eliminate the need for the Higgs potential and the associated hierarchy problem. We also show that the axial anomaly formula at z=3 coincides with the usual one in the relativistic domain.