论文标题
比例对称性的自发对称分解
Spontaneous Symmetry Breakdown of Scale Symmetries
论文作者
论文摘要
我们讨论了标量调节引力的全局和局部规模对称性的自发对称分解（SSB），其中两个标量场磁场与标量曲率非小构相结合，而另一个则是正常的标量场。在全球尺度对称性的情况下，通过从约旦框架移动到爱因斯坦框架，正常的标量场变得巨大，而DILATON在SSB之后保持无质量。在局部规模对称性的情况下，我们为局部规模不变性采取量规固定条件，$ a r + b ϕ^2 = k $，这是在我们先前对Weyl二次引力的研究中发现的。该规格条件在经典作用中与局部规模不变的潜在术语一起产生了Higgs潜力，其真空期望值（VEV）在最低近似水平的$ r^2 $项中产生Einstein-Hilbert Action。该模型中一个有趣的方面是，与量表不变性相关的无质量nambu-goldstone玻色子被吸收到公制张量场中，因此在动作中引起了$ r^2 $项。
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.
