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...e extended to AdS6 as well. In D = 3 the HS gauge fields do not propagate physical degrees of freedom. Nonetheless, physical matter fields of spin s = 0,1/2 can be coupled to massless HS gauge theory =-=[92, 93]-=-. The advantage here is that an action principle is known and the mathematics is much simpler than in higher dimensions. It would be interesting to study this model in the context of massless higher s...

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...asiliev first in AdS4 [112], and then generalised to other dimensions including AdS3 [113, 114]. In 3d, they are labelled by a single parameter µ and based on a higher spin gauge group known as hs[µ] =-=[103, 104]-=-; we summarise some of the relevant facts about these theories and their symmetries in Sec. 2.1. As is familiar from the classic calculation of Brown & Henneaux [27], partial information about the dua...

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... [5, 6, 7, 8, 9, 10]. It is primarily with the above motivations in mind that we have sought and found an exact solution beyond AdS spacetime. In doing so, we have greatly benefitted from the work of =-=[11, 12, 13]-=-. In [11] an exact solution is given for a higher-spin gauge theory in 3D. In [12], plane-wave solutions for the free 4D field equations are provided, and [13] proposes an interesting method pertinent...

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...gravitational sector it allows for a richer space of solutions, still without gravitational waves but with black holes [7]. It also allows to build three-dimensional counterparts of Vasiliev’s models =-=[8]-=-, describing the coupling of two or four scalars to a HS gauge sector. The latter toy models provide a natural arena to test – with suitable extrapolations – various proposals that relate holographica...

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... 10 A. Basics of so(2N) 13 A.1 The Weyl denominator formula 16 B. The fusion calculation 17 B.1 Going up to level one 18 1. Introduction Recently, a duality between a higher spin gauge theory on AdS3 =-=[1, 2]-=-, and the large N ’t Hooft limit of a family of WN minimal models has been proposed [3]. This proposal is the natural 3d/2d analogue of the Klebanov-Polyakov duality [4] (see also [5, 6, 7] for earlie...

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... higher-spin gauge fields. The projection to the fiber, on the other hand, is a more tractable operation, since the Vasiliev equations can be solved locally on the base manifold using gauge functions =-=[4]-=-. This leaves equations on the non-commutative fiber, which are thus purely algebraic from the point-of-view of the base manifold. The simplest exact solution to these equations is the four-dimensiona...

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...ging to it at ν = d(d+1)8 and at the “singleton point” ν = − (d−1)(d−3)4 , respectively. The algebra hs(ν) can be thought of as a generalization to arbitrary dimension of the 3d higherspin algebra of =-=[53]-=-, which is based on the deformed oscillator algebra [54]. Recently there has 1See [48–50] for more detailed exposition and original results. 3 been a lot of interest in 3d hs(ν) in the context of AdS3...