Supersymmetric holography on AdS3

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: The General N Case: Cpsupporting

confidence: 63%

Section: Introductionmentioning

confidence: 99%

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

Ahn

2012

“…This has been worked out in [6,19] (see [27] for a similar analysis for the bosonic models) by using large level expansions of the individual character that enter (2.5) as we will review below.…”

Section: Limit Of Coset Charactersmentioning

confidence: 99%

The large level limit of Kazama-Suzuki models

Fredenhagen

Restuccia

2015

Limits of families of conformal field theories are of interest in the context of AdS/CFT dualities. We explore here the large level limit of the two-dimensional N = (2, 2) superconformal W n+1 minimal models that appear in the context of the supersymmetric higher-spin AdS 3 /CFT 2 duality. These models are constructed as Kazama-Suzuki coset models of the form SU(n + 1)/U(n). We determine a family of boundary conditions in the limit theories, and use the modular bootstrap to obtain the full bulk spectrum of N = 2 super-W n+1 primaries in the theory. We also confirm the identification of this limit theory as the continuous orbifold C n /U(n) that was discussed recently.

“…All conserved quantities of the Boussinesq equation in x − evolution can be expressed as 22) for any positive integer k ≥ 1 and k = 3N, where Res(·) denotes the residue or term proportional to ∂ −1 + in the argument. Remark that ∂ + -exact terms in h k do not contribute to the conserved charges.…”

Section: Commuting Charges From the Kdv Hierarchymentioning

confidence: 99%

“…Partition functions have been computed in [15,16], and three point functions have been checked in [7,[17][18][19]. Other aspects of the duality have been investigated extensively [20][21][22][23][24][25], see [26] for a review.…”

Section: Introductionmentioning

confidence: 99%

$ \mathcal{W} $ symmetry and integrability of higher spin black holes

Compère

Song²

2013

We obtain the asymptotic symmetry algebra of sl(3, R) × sl(3, R) Chern-Simons theory with Dirichlet boundary conditions for fixed chemical potential. These boundary conditions are obeyed by higher spin black holes. For each embedding of sl(2, R) into sl(3, R), we show that the asymptotic symmetry group is independent of the chemical potential. On the one hand, starting from AdS 3 in the principal embedding, we show that the W 3 × W 3 symmetry is preserved upon turning on perturbatively spin 3 chemical potentials. On the other hand, starting from AdS 3 in the diagonal embedding, we show that the W (2) 3 ×W (2) 3 symmetry is preserved upon turning on finite spin 3/2 chemical potentials. We also make connections between the canonical Lagrangian formalism and integrability methods based on the n = 3 KdV (Boussinesq) hierarchy.