On higher spin symmetries in de Sitter QFTs

Costa, Renato Nunes; Morrison, Ian A.

doi:10.1007/jhep03(2016)056

Cited by 2 publications

(2 citation statements)

References 41 publications

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“…As suggested by the notation, the generators :Φ ⊗k : M (u) ∈ W(M ) are (distributionally) smeared k-multilocal fields, Wick ordered with respect to W M . 8 Owing to (14), they do not transform covariantly for k > 1, because there is no choice of W M such that (ψ × ψ) * W N = W M for all ψ : M → N . However, locally covariant Wick powers can be defined as follows.…”

Section: Action On Local Wick Powers Scaling Induces a Group Action Omentioning

confidence: 99%

“…The CM theorem concerns a particular spacetime of high symmetry. For a generic spacetime with trivial isometry group, it is obvious that the internal and geometric symmetries combine as a direct product, and one might think that the CM theorem has nothing to say except for spacetimes of high symmetry (see [8] for a recent CM analogue in de Sitter spacetime). However, the viewpoint of locally covariant QFT suggests a different approach.…”

Section: Introductionmentioning

confidence: 99%

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An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

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Abstract:The Coleman-Mandula (CM) theorem states that the Poincaré and internal symmetries of a Minkowski spacetime quantum field theory cannot combine nontrivially in an extended symmetry group. We establish an analogous result for quantum field theory in curved spacetimes, assuming local covariance, the timeslice property, a local dynamical form of Lorentz invariance, and additivity. Unlike the CM theorem, our result is valid in dimensions n ≥ 2 and for free or interacting theories. It is formulated for theories defined on a category of all globally hyperbolic spacetimes equipped with a global coframe, on which the restricted Lorentz group acts, and makes use of a general analysis of symmetries induced by the action of a group G on the category of spacetimes. Such symmetries are shown to be canonically associated with a cohomology class in the second degree nonabelian cohomology of G with coefficients in the global gauge group of the theory. Our main result proves that the cohomology class is trivial if G is the universal cover S of the restricted Lorentz group. Among other consequences, it follows that the extended symmetry group is a direct product of the global gauge group and S, all fields transform in multiplets of S, fields of different spin do not mix under the extended group, and the occurrence of noninteger spin is controlled by the centre of the global gauge group. The general analysis is also applied to rigid scale covariance.

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Section: Action On Local Wick Powers Scaling Induces a Group Action Omentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Fewster

2017

Commun. Math. Phys.

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Hidden symmetries for transparent de Sitter space

Compton

Morrison

2020

Class. Quantum Grav.

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It is known that odd-dimensional de Sitter space acts as a transparent potential for free fields. Previous studies have explained this phenomena by relating de Sitter free field equations of motion to the time-independent Schrodinger equation with known transparent potentials. In this work we show that de Sitter's transparency is a consequence of an infinite set of 'hidden' symmetries. These symmetries arise from an accidental symmetry for the zero-mode of matter fields, as well as the boost isometry of de Sitter space. For simplicity, we consider the case of massive Klein-Gordon theory. We show that the Noether charges associated with these hidden symmetries distinguish the two linearly-independent solutions of the free field wave equation in the asymptotic past and future of de Sitter. Conservation of these charges requires that the asymptotic behavior of any solution be identical, up to a constant phase, in the future and the past, which is the property of transparency. In the quantized theory, these charges act trivially on particle states belonging to the in/out vacuum Fock space. For particle states constructed from other vacua, the action of the charges generates particles. We comment on how these hidden symmetries may be present in interacting theories.

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On higher spin symmetries in de Sitter QFTs

Cited by 2 publications

References 41 publications

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

An Analogue of the Coleman–Mandula Theorem for Quantum Field Theory in Curved Spacetimes

Hidden symmetries for transparent de Sitter space

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