The large N ’t Hooft limit of coset minimal models

Abstract

Recently, Gaberdiel and Gopakumar proposed that the two-dimensional W A N −1 minimal model conformal field theory in the large N 't Hooft limit is dual to the higher spin theories on the three-dimensional AdS space with two complex scalars. In this paper, we examine this proposal for the W D N 2 and W B N−1 2 minimal models initiated by Fateev and Lukyanov in 1988. By analyzing the renormalization group flows on these models, we find that the gravity duals in AdS space are higher spin theories coupled to two equally massive real scalar fields. We also describe the large N 't Hooft limit for the minimal model of the second parafermion theory.

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

“…Then the standard Sugawara construction can follow similarly, along the line of [37]. See also the relevant works in [38,39].…”

“…The self-coupling constant of the current with spins (2, 5 2 , 5 2 , 3) for any N = 2 W N +1 algebra is determined from the unitarity arguments in [15] 38) where the central charge is given by (2.14). Note that the previous constants (2.22) and (2.27) can be read off from this general expression (2.38) by substituting N = 2 and N = 4…”

Supersymmetric holography on AdS3

“…The proposal of [29] was generalised to the case where instead of the su(N ) based W -algebras, one considers the so(2N ) series [42,43]. More recently, a N = 2 supersymmetric generalisation has been proposed [44], relating a family of Kazama-Suzuki models [45,46] to the supersymmetric higher spin theory of [22,23].…”

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

“…The conjecture relates the Vasiliev theory to a large N limit of W N minimal models at fixed 't Hooft coupling λ where λ is the deformation parameter of the hs(λ) bulk algebra (see [6][7][8][9][10][11][12][13][14] for further refinements and extensions of the original conjecture). Partition functions have been computed in [15,16], and three point functions have been checked in [7,[17][18][19].…”