Extended higher spin holography and Grassmannian models

Abstract

We propose holographic dualities between higher spin gravity theories extended with Chan-Paton factor on AdS 3 and a large N limit of two dimensional Grassmannian models with and without supersymmetry. These proposals are natural extensions of the duality without Chan-Paton factor, and the extensions are motivated by a higher dimensional version of the duality, which implies a possible relation to superstring theory via ABJ theory. As evidence for the proposals, we show that the free limit of the Grassmannian models have the higher spin symmetry expected from the dual gravity theory. Furthermore, we construct currents in the 't Hooft limit of the supersymmetric Grassmannian model and compare them with the currents from the bulk theory. One-loop partition function of the supergravity theory is reproduced by the 't Hooft limit of the Grassmannian model after decoupling a gauge sector.

The large $ \mathcal{N} $ = 4 superconformal $ \mathcal{W} $ ∞ algebra

“…The proposal of [10] was subsequently explored further. In particular, the spectrum of the two descriptions was matched in [15], see also [16] for an earlier analysis, and the asymptotic symmetry algebra of the higher spin theory was shown to agree with the 't Hooft limit of the Wolf space coset W algebras [17]. While many of the features of this duality mirror precisely what happens for the original bosonic proposal [4] and its N = 2 supersymmetric generalisation [18,19], there is one intriguing difference that was already noticed in [10]: while the quantum W ∞ algebras underlying the bosonic and the N = 2 version exhibit a triality or quadrality relation [20,21], respectively, that explains the identification of the quantisation of the asymptotic symmetry algebra with the dual coset algebra even at finite N , a similar relation does not seem to exist in the large N = 4 case.…”

Higher spins in the symmetric orbifold of K3

“…(the reader is encouraged to consult [21] for more details); further evidence for this duality was given in [22,23,24,25,26].…”

Three Point Functions in Higher Spin AdS3 Holography with 1/N Corrections

“…Recently, it becomes possible to discuss relations between 3d higher spin theory and superstrings by introducing extended supersymmetry to the duality by [1]. Higher spin holography with N = 3 supersymmetry has been developed in a series of works [29][30][31], while large or small N = 4 supersymmetry has been utilized through the well-studied holography with symmetric orbifold in [32,33]. Previous works on the subject may be found in [34][35][36].…”