The continuous orbifold of N $$ \mathcal{N} $$ = 2 minimal model holography

Abstract

For the N = 2 Kazama-Suzuki models that appear in the duality with a higher spin theory on AdS 3 it is shown that the large level limit can be interpreted as a continuous orbifold of 2N free bosons and fermions by the group U(N ). In particular, we show that the subset of coset representations that correspond to the perturbative higher spin degrees of freedom are precisely described by the untwisted sector of this U(N ) orbifold. We furthermore identify the twisted sector ground states of the orbifold with specific coset representations, and give various pieces of evidence in favour of this identification.

The large level limit of Kazama-Suzuki models

“…(2.10)). 3 In [19] a class of coset fields was identified whose conformal weights, which could be computed exactly, precisely match the conformal weights we expect for the ground states of the twisted sector of the continuous orbifold theory that is supposed to describe the limit theory. We take this identification as a starting point to formulate a proposal for what happens to the complete bulk spectrum in the limit.…”

“…Analogously, it was conjectured in [18] that the large level limit for general n is given by the continuous orbifold C n /U(n). Recently, evidence for this conjecture has been given in [19], where the untwisted sector as well as the ground states of the twisted sectors of the orbifold theory were identified in the limit theory. In the present work we on the one hand give further support to the conjecture by an analysis of boundary conditions and boundary partition functions, and on the other hand we provide a complete description of the spectrum of N = 2 W n+1 -primaries in the limit theory, which is based on the modular bootstrap.…”

“…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.…”

“…[29], appendix A) 19) we can explicitly solve the integral (3.16). We find 20) recalling that L + M must be even (L, M are u(2) representation labels).…”

“…We expect that in the limit the representation labels of bulk fields have to be scaled with k. Following [19], we write the labels λ, µ of the denominator group as 4…”