Super-W∞ asymptotic symmetry of higher-spin AdS3 supergravity

We consider N = 2 Kazama-Suzuki model on CP N = SU (N +1) SU (N )×U (1) . It is known that the N = 2 current algebra for the supersymmetric WZW model, at level k, is a nonlinear algebra. The N = 2 W 3 algebra corresponding to N = 2 was recovered from the generalized GKO coset construction previously. For N = 4, we construct one of the higher spin currents, in N = 2 W 5 algebra, with spins (2, 5 2 , 5 2 , 3). The self-coupling constant in the operator product expansion of this current and itself depends on N as well as k explicitly. We also observe a new higher spin primary current of spins (3, 7 2 , 7 2 , 4). From the behaviors of N = 2, 4 cases, we expect the operator product expansion of the lowest higher spin current and itself in N = 2 W N +1 algebra. By taking the large (N, k) limit on the various operator product expansions in components, we reproduce, at the linear order, the corresponding operator product expansions in N = 2 classical W cl ∞ [λ] algebra which is the asymptotic symmetry of the higher spin AdS 3 supergravity found recently.

Section: Discussionmentioning

confidence: 99%

The large N ’t Hooft limit of Kazama-Suzuki model

Ahn

2012

“…This work brings in many open problems worth of further investigation. First of all, extensions to (higher-spin) supergravity as well as the analysis of the asymptotic symmetries [48][49][50] are imminent. Further extensions to color-decoration of the known higherspin gravity in three-dimensional Lifshitz spacetime [51] and flat spacetime [52,53] are also straightforward.…”

Section: Jhep04(2016)055mentioning

confidence: 99%

Rainbow valley of colored (anti) de Sitter gravity in three dimensions

Gwak

Joung

Mkrtchyan

et al. 2016

Self Cite

We propose a theory of three-dimensional (anti) de Sitter gravity carrying Chan-Paton color charges. We define the theory by Chern-Simons formulation with the gauge algebra (gl 2 ⊕ gl 2 ) ⊗ u(N ), obtaining a color-decorated version of interacting spinone and spin-two fields. We also describe the theory in metric formulation and show that, among N 2 massless spin-two fields, only the singlet one plays the role of metric graviton whereas the rest behave as colored spinning matter that strongly interacts at large N . Remarkably, these colored spinning matter acts as Higgs field and generates a non-trivial potential of staircase shape. At each extremum labelled by k = 0, . . . , [ N −1 2 ], the u(N ) color gauge symmetry is spontaneously broken down to u(N − k) ⊕ u(k) and provides different (A)dS backgrounds with the cosmological constants N N −2k 2 Λ. When this symmetry breaking takes place, the spin-two Goldstone modes combine with (or are eaten by) the spin-one gauge fields to become partially-massless spin-two fields. We discuss various aspects of this theory and highlight physical implications.

“…This duality has also been checked by comparison of the symmetries and the partition function [15,16]. Chern-Simons theories based on super-extended higher spin super algebras have been considered in [17] and their asymptotic algebras have been shown to agree with the corresponding super conformal W ∞ algebra. Studying classical solutions in Chern-Simons theories based on a higher spin group provides more more insights to holography in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

Supersymmetry of classical solutions in Chern-Simons higher spin supergravity

Datta

David²

2013

We construct and study classical solutions in Chern-Simons supergravity based on the superalgebra sl(N|N − 1). The algebra for the N = 3 case is written down explicitly using the fact that it arises as the global part of the super conformal W 3 superalgebra. For this case we construct new classical solutions and study their supersymmetry. Using the algebra we write down the Killing spinor equations and explicitly construct the Killing spinor for conical defects and black holes in this theory. We show that for the general sl(N|N − 1) theory the condition for the periodicity of the Killing spinor can be written in terms of the products of the odd roots of the super algebra and the eigenvalues of the holonomy matrix of the background. Thus the supersymmetry of a given background can be stated in terms of gauge invariant and well defined physical observables of the Chern-Simons theory. We then show that for N ≥ 4, the sl(N|N −1) theory admits smooth supersymmetric conical defects.