| 1. |
- Linander, Hampus, 1985, et al.
(författare)
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The non-linear coupled spin 2 - spin 3 Cotton equation in three dimensions
- 2016
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2016:7
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Tidskriftsartikel (refereegranskat)abstract
- In the context of three-dimensional conformal higher spin theory we derive, in the frame field formulation, the full non-linear spin 3 Cotton equation coupled to spin 2. This is done by solving the corresponding Chern-Simons gauge theory system of equations, that is, using F=0 to eliminate all auxiliary fields and thus expressing the Cotton equation in terms of just the spin 3 frame field and spin 2 covariant derivatives and tensors (Schouten). In this derivation we neglect the spin 4 and higher spin sectors and approximate the star product commutator by a Poisson bracket. The resulting spin 3 Cotton equation is complicated but can be related to linearized versions in the metric formulation obtained previously by other authors. The expected symmetry (spin 3 "translation", "Lorentz" and "dilatation") properties are verified for Cotton and other relevant tensors but some perhaps unexpected features emerge in the process, in particular in relation to the non-linear equations. We discuss the structure of this non-linear spin 3 Cotton equation but its explicit form is only presented here, in an exact but not completely refined version, in appended files obtained by computer algebra methods. Both the frame field and metric formulations are provided.
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| 2. |
- Nilsson, Bengt E W, 1952
(författare)
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On the conformal higher spin unfolded equation for a three-dimensional self-interacting scalar field
- 2016
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2016:8, s. 142-
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Tidskriftsartikel (refereegranskat)abstract
- We propose field equations for the conformal higher spin system in three dimensions coupled to a conformal scalar field with a sixth order potential. Both the higher spin equation and the unfolded equation for the scalar field have source terms and are based on a conformal higher spin algebra which we treat as an expansion in multi-commutators. Explicit expressions for the source terms are suggested and subjected to some simple tests. We also discuss a cascading relation between the Chern-Simons action for the higher spin gauge theory and an action containing a term for each spin that generalizes the spin 2 Chern-Simons action in terms of the spin connection expressed in terms of the frame field. This cascading property is demonstrated in the free theory for spin 3 but should work also in the complete higher spin theory.
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| 3. |
- Nilsson, Bengt E W, 1952, et al.
(författare)
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The role of singletons in S 7 compactifications
- 2019
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2019:7
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Tidskriftsartikel (refereegranskat)abstract
- We derive the isometry irrep content of squashed seven-sphere compactifications of eleven-dimensional supergravity, i.e., the left-squashed (LS7) with N = 1 and right-squashed (RS7) with N = 0 supersymmetry, in a manner completely independent of the round sphere. Then we compare this result with the spectrum obtained by Higgsing the round sphere spectrum. This way we discover features of the spectra which makes it possible to argue that the only way the round spectrum can be related by a Higgs mechanism to the one of LS7 is if the singletons are included in the round sphere spectrum. For this to work also in the RS7 case it seems that the gravitino of the LS7 spectrum must be replaced by a fermionic singleton present in the RS7 spectrum.
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| 4. |
- Nilsson, Bengt E W, 1952
(författare)
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Towards an exact frame formulation of conformal higher spins in three dimensions
- 2015
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Ingår i: Journal of High Energy Physics. - 1029-8479 .- 1126-6708. ; 2015:9, s. Art. no. 78-
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Tidskriftsartikel (refereegranskat)abstract
- In this note we discuss some aspects of the frame formulation of conformal higher spins in three dimensions. We give some exact formulae for the coupled spin two - spin three part of the full higher spin theory and propose a star product Lagrangian for all spins from two and up. Since there is no consistent Lagrangian formulation based on the Poisson bracket we start the construction from the field equations in this approximation of the star product. The higher spin algebra is then realized in terms of classical variables which leads to certain important simplifications that we take advantage of. The suggested structure of the all-spin Lagrangian given here is, however, obtained using an expansion of the star product beyond the Poisson bracket in terms of multi-commutators and the Lagrangian should be viewed as a starting point for the derivation of the full theory based on a star product. How to do this is explained as well as how to include the coupling to scalar fields. We also comment on the AdS/CFT relation to four dimensions.
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