Higher spins and Yangian symmetries

193

We analyze the asymptotic symmetry of higher spin gravity with M × M matrix valued fields, which is given by rectangular W-algebras with su(M ) symmetry. The matrix valued extension is expected to be useful for the relation between higher spin gravity and string theory. With the truncation of spin as s = 2, 3, . . . , n, we evaluate the central charge c of the algebra and the level k of the affine currents with finite c, k. For the simplest case with n = 2, we obtain the operator product expansions among generators by requiring their associativity. We conjecture that the symmetry is the same as that of Grassmannian-like coset based on our proposal of higher spin holography. Comparing c, k from the both theories, we obtain the map of parameters. We explicitly construct low spin generators from the coset theory, and, in particular, we reproduce the operator product expansions of the rectangular W-algebra for n = 2. We interpret the map of parameters by decomposing the algebra in the coset description.

Section: Decomposition Of Rectangular W-algebramentioning

confidence: 99%

“…we can use arbitrary c 6 , c 53 , c 72 , c 42 , c73 . There are more relations asd 3if ab (c δ de) , d abcd 4AA1 = 2(δ ac δ bd − δ ad δ bc ) , d abcd 4SS1 = 2δ ab δ cd , d abcd 4SS2 = −2δ ab δ cd + 2(δ ac δ bd + δ ad δ bc ) .…”

mentioning

confidence: 99%

Rectangular W-algebras, extended higher spin gravity and dual coset CFTs

Creutzig

Hikida

2019

193

“…Remarkably, these assumptions lead to highly constrained interactions governed by non-abelian higher spin symmetry algebras, whose consistency requires special matter sectors and non-vanishing cosmological constant. The resulting framework thus provides a natural platform for studying tensionless string theory in anti-de Sitter spacetime [21][22][23] (for recent advances, see [24][25][26]) and holography [21,[27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] (for a different approach, see also [42]), without relying on any a priori assumptions on dualities between strong and weak coupling on the worldsheet or the conformal field theory side. One of the outstanding problems is to connect two different approaches to higher spin gravity that are presently pursued: Vasiliev's theory and the quasi-local deformed Fronsdal theory.…”

Section: Motivationsmentioning

confidence: 99%

4D higher spin black holes with nonlinear scalar fluctuations

Iazeolla

Sundell

2017

216

Abstract:We construct an infinite-dimensional space of solutions to Vasiliev's equations in four dimensions that are asymptotic to AdS spacetime and superpose massless scalar particle modes over static higher spin black holes. Each solution is obtained by a large gauge transformation of an all-order perturbatively defined particular solution given in a simple gauge, in which the spacetime connection vanishes, the twistor space connection is holomorphic, and all local degrees of freedom are encoded into the residual twistor space dependence of the spacetime zero-forms. The latter are expanded over two dual spaces of Fock space operators, corresponding to scalar particle and static black hole modes, equipped with positive definite sesquilinear and bilinear forms, respectively. Switching on an AdS vacuum gauge function, the twistor space connection becomes analytic at generic spacetime points, which makes it possible to reach Vasiliev's gauge, in which Fronsdal fields arise asymptotically, by another large transformation given here at first order. The particle and black hole modes are related by a twistor space Fourier transform, resulting in a black hole backreaction already at the second order of classical perturbation theory. We speculate on the existence of a fine-tuned branch of moduli space that is free from black hole modes and directly related to the quasi-local deformed Fronsdal theory. Finally, we comment on a possible interpretation of the higher spin black hole solutions as black-hole microstates.

“…where R runs over all representations that appear in finite tensor powers of the two bi-minimal representations, andR T is the conjugate representation to R T , with T denoting the transpose of R. Since R involves in general box and anti-box representations, and since the wedge character of such a mixed representation is simply the product of the wedge character of the box representation and that of the anti-box representation, the above identity follows from 20) where S runs over all Young diagrams (labelling say box-representations), S T is the transpose Young diagram (labelling now anti-box representations), and |S| denotes the number of boxes in S. The first few cases are explicitly (see [36] for the general method for how to derive them)…”

Section: Character Analysismentioning

confidence: 99%

“…Integrable theories are usually distinguished by having a Yangian symmetry, and one may therefore try to identify the relevant Yangian in the explicit higher spin description. This was recently done [19,20] for the bosonic toy model of [13], where the generators of W ∞ [λ], the symmetry algebra of the higher spin theory, were explicitly identified with those of the affine Yangian of gl 1 . (The underlying isomorphism was first noted in [21,22], generalizing the construction of [23], and independently by [24] and [25][26][27], see also [28] for further generalizations.…”

mentioning

confidence: 99%

The supersymmetric affine Yangian

Gaberdiel

Peng

et al. 2018

Self Cite

109

The affine Yangian of gl 1 is known to be isomorphic to W 1+∞ , the Walgebra that characterizes the bosonic higher spin -CFT duality. In this paper we propose some of the defining relations of the Yangian that are relevant for the N = 2 superconformal version of W 1+∞ . Our construction is based on the observation that the N = 2 superconformal W 1+∞ algebra contains two commuting bosonic W 1+∞ algebras, and that the additional generators transform in bi-minimal representations with respect to these two algebras. The corresponding affine Yangian can therefore be built up from two affine Yangians of gl 1 by adding in generators that transform appropriately.