Abstract
In 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.
Highlights
The first concerns the elimination itself, which is often performed by imposing socalled inverse Higgs constraints
After reviewing the most important aspects of the coset construction for both internal and spacetime symmetry breaking in section 2, in section 3 we present the conditions on the structure constants which must be satisfied in order to employ the inverse Higgs phenomenon
In any case we show that as long as the series of inverse Higgs conditions are met, the effective field theory constructed from only the essential Goldstone fields is the same, up to variations in coupling constants which are not fixed by symmetry, regardless of how one chooses to eliminate the inessential Goldstones
Summary
We review the coset construction as a tool for constructing non-linear realisations. We begin with the case where the non-linearly realised symmetry is an internal one i.e. the generators commute with those of the Poincare group, we move onto spontaneously broken spacetime symmetries.
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