2016
DOI: 10.1007/s00220-016-2712-x
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Higher Spins from Nambu–Chern–Simons Theory

Abstract: Abstract:We propose a new theory of higher spin gravity in three spacetime dimensions. This is defined by what we will call a Nambu-Chern-Simons (NCS) action; this is to a Nambu 3-algebra as an ordinary Chern-Simons (CS) action is to a Lie (2-)algebra. The novelty is that the gauge group of this theory is simple; this stands in contrast to previously understood interacting 3D higher spin theories in the frame-like formalism. We also consider the N = 8 supersymmetric NCS-matter model (BLG theory), where the NCS… Show more

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Cited by 5 publications
(4 citation statements)
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References 71 publications
(203 reference statements)
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“…It starts from a genuine Lie algebra g (that we can view as the global symmetry of the 'ungauged phase') and an embedding tensor, that in 3D is a symmetric tensor Θ on the dual space g ˚. 9 There is another 3D Chern-Simons-type theory with an infinite-dimensional extension of the AdS algebra that does not factorize [49]. This is based on the algebra of volume preserving diffeomorphisms on S 3 [50], which is a genuine Lie algebra that, however, does not have an invariant quadratic form.…”
Section: Discussionmentioning
confidence: 99%
“…It starts from a genuine Lie algebra g (that we can view as the global symmetry of the 'ungauged phase') and an embedding tensor, that in 3D is a symmetric tensor Θ on the dual space g ˚. 9 There is another 3D Chern-Simons-type theory with an infinite-dimensional extension of the AdS algebra that does not factorize [49]. This is based on the algebra of volume preserving diffeomorphisms on S 3 [50], which is a genuine Lie algebra that, however, does not have an invariant quadratic form.…”
Section: Discussionmentioning
confidence: 99%
“…In most known examples, the higher spin Lie algebra h can be embedded in an associative algebra a, such that the Lie bracket in h arises from the commutator in a. If this is the case, we can write down linearized equations 3 for two scalar matter fields 2 See however [11] for an example of a higher spin theory based on a Lie algebra which is simple, rather than a product of two isomorphic copies. 3 In the original work [10], see also [16], the equations were written more succinctly by introducing an extra Grassmann element φ, satisfying φ 2 = 1, and the associated projection operators P± = 1±φ 2 .…”
Section: Linearized Matter Equationsmentioning
confidence: 99%
“…The q-Virasoro constraints for this matrix model have been derived by the insertion of the q-Virasoro generators under the contour integral [15], where the q-Virasoro generators are constructed in terms of q-derivatives within the q-calculus and the corresponding q-Virasoro algebra is a special case of a more general elliptic deformation of the Virasoro algebra [16]. Since 3-algebra has recently been found useful in the Bagger-Lambert-Gustavsson (BLG) theory of M2-branes [17,18], the applications of n-algebra have aroused much interest [19]- [25]. More recently it was found that there are the generalized q-W ∞ constraints for the elliptic matrix model [26].…”
Section: Introductionmentioning
confidence: 99%