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

Abstract

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.

Minimal model holography

“…However, we can satisfy the Jacobi identities exactly, i.e. for arbitrary finite c, by (i) defining carefully what we mean by Λ (4) , Λ (5) , Θ (6) , i.e. by specifying the correct 'normal ordering prescription'; and (ii) by modifying the above commutation relations by 1/c corrections.…”

“…It was observed in [1] that the flatness conditions F a ≡ dA a + ǫ a bc A b ∧ A c = 0 and F a = 0 that arise as equations of motion from (7) are in fact equivalent to the Einstein equations of pure gravity (4) and (5). In a similar vein, it was shown in [117] that the Chern-Simons action (7) reduces, up to some boundary terms, to the Einstein-Hilbert action (with negative cosmological constant) provided we identifŷ…”

“…Other states, including those dual to h − and the 'light' states, are to be viewed as conical defects (and their generalisations) bound with perturbative quanta [100]; all of this will be discussed in Sec. 5.…”

The OPEs of spin-4 Casimir currents in the holographic SO ( N ) coset minimal models

“…So far, the supersymmetric versions of minimal model holography are described in the recent works [40,41,42,43,32,44,33,45,46,47,48,49,50]. In particular, it would be interesting to see whether the W B N−1 2 minimal model can be generalized to the supersymmetric extension or not.…”

“…7 We have checked the OPE (3.2) when N = 6 and realize that the result is exactly the same as ( Then the OPE (3.2) under the large (N, k) limit can be obtained by substituting (3.12) and (3.13) into (3.2). See also the related works [32,33] where the large (N, k) 't Hooft limit on the OPE was described.…”