Spontaneously broken spacetime symmetries and the role of inessential Goldstones
Spontaneously broken spacetime symmetries and the role of inessential Goldstones
复制标题
自发破缺的时空对称性和无关紧要的戈德斯通的作用
DOI：
--
复制
发表时间：
2017
期刊：
影响因子：
--
通讯作者：
David Stefanyszyn
中科院分区：
文献类型：
--
作者：
Remko Klein;D. Roest;David Stefanyszyn
与内部对称性不同，没有普遍的证据证明自发破缺的时空对称性的陪集结构导致了宇宙动力学。一个关键的区别在于戈德斯通玻色子的作用，对于时空对称性，它包括一个对非线性实现不必要的子集，因此可以消除。在这篇文章中，我们讨论了消除无关紧要的Goldstone时出现的两个重要问题。第一个涉及消除本身，这通常是通过施加所谓的逆Higgs约束来实现的。与文献中的说法相反，有一系列关于结构常数的条件必须满足才能使用逆Higgs现象，我们讨论了陪集元素的哪个参数在这方面是最有效的。我们还考虑了标准逆Higgs约束的推广，它可以包括在低能量下积分不重要的Goldstone，并证明在某些假设下，这些推广可以得到本质Goldstone的相同的有效场论。其次，我们考虑在陪集元素和代数基上都不同的非线性实现之间的映射。虽然这些约束总是可以通过点变换相互关联，但值得注意的是，在这种变换下，逆希格斯约束不一定相互映射。我们讨论了这种非映射的物理含义，特别强调了与Minkowski探针膜自发破坏anti-de Sitter等距相对应的陪集空间。
A bstractIn contrast to internal symmetries, there is no general proof that the coset construction for spontaneously broken spacetime symmetries leads to universal dynamics. One key difference lies in the role of Goldstone bosons, which for spacetime symmetries includes a subset which are inessential for the non-linear realisation and hence can be eliminated. In this paper we address two important issues that arise when eliminating inessential Goldstones.The first concerns the elimination itself, which is often performed by imposing so-called inverse Higgs constraints. Contrary to claims in the literature, there are a series of conditions on the structure constants which must be satisfied to employ the inverse Higgs phenomenon, and we discuss which parametrisation of the coset element is the most effective in this regard. We also consider generalisations of the standard inverse Higgs constraints, which can include integrating out inessential Goldstones at low energies, and prove that under certain assumptions these give rise to identical effective field theories for the essential Goldstones.Secondly, we consider mappings between non-linear realisations that differ both in the coset element and the algebra basis. While these can always be related to each other by a point transformation, remarkably, the inverse Higgs constraints are not necessarily mapped onto each other under this transformation. We discuss the physical implications of this non-mapping, with a particular emphasis on the coset space corresponding to the spontaneous breaking of the Anti-De Sitter isometries by a Minkowski probe brane.