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arXiv 2003.07947hep-thgr-qchep-ph
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标度对称性的自发对称性破缺

Spontaneous Symmetry Breakdown of Scale Symmetries

Ichiro Oda

摘要:

讨论了具有两个标量场的标量-张量引力中的整体和局部尺度对称性的自发对称性破缺(SSB),其中一个标量场非极小地耦合到标量曲率上,另一个标量场是正常的标量场.在整体尺度对称的情况下,通过从约当框架移动到爱因斯坦框架,正常的标量场变得有质量,而在SSB之后,标量子保持无质量。在局域尺度对称的情况下,我们采用了规范固定条件,用于局域尺度不变性,$a R + b ϕ^2 = k$,这是在我们以前研究Weyl二次引力时发现的。与经典作用量中的定域标度不变势项一起,这个规范条件产生了一个希格斯势,其真空期望值(VEV)产生了具有最低近似水平的$R^2$项的爱因斯坦-希尔伯特作用量。在这个模型中,一个有趣的方面是,一个无质量的Nambu-Goldstone玻色子与标度不变性被吸收到度规张量场,因此一个$R^2$长期诱导的行动。

英文摘要:

We discuss spontaneous symmetry breakdown (SSB) of both global and local scale symmetries in scalar-tensor gravity with two scalar fields, one of which couples nonminimally to scalar curvature while the other is a normal scalar field. In case of a global scale symmetry, by moving from the Jordan frame to the Einstein frame, a normal scalar field becomes massive while the dilaton remains massless after the SSB. In case of a local scale symmetry, we take a gauge fixing condition for the local scale invariance, $a R + b ϕ^2 = k$, which was found in our previous study of a Weyl's quadratic gravity. Together with locally scale invariant potential terms in a classical action, this gauge condition generates a Higgs potential whose vacuum expectation value (VEV) produces the Einstein-Hilbert action with an $R^2$ term in the lowest level of approximation. One interesting aspect in this model is that a massless Nambu-Goldstone boson associated with a scale invariance is absorbed into the metric tensor field and consequently an $R^2$ term is induced in the action.

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。

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