Abstract
The large level limit of the N=2 minimal models that appear in the duality with the N=2 supersymmetric higher spin theory on AdS_3 is shown to be a natural subsector of a certain symmetric orbifold theory. We study the relevant decompositions in both the untwisted and the twisted sector, and analyse the structure of the higher spin representations in the twisted sector in some detail. These results should help to identify the string background of which the higher spin theory is expected to describe the leading Regge trajectory in the tensionless limit.
Highlights
Dualities may be related naturally to string theory
In this paper we follow a different route by trying to imitate the analysis of [6] for the N = 2 case: following on from our earlier work [23], where we showed that the large level limit of the relevant KS models can be described as the continuous orbifold of a free theory, we discuss how this free theory is related to a symmetric orbifold construction
A similar approach was applied to the N = 4 Wolf space cosets in [6], where it was shown that the corresponding coset algebra is a natural subalgebra of the chiral algebra of the symmetric orbifold; in turn the symmetric orbifold is believed to be dual to string theory on AdS3, exhibiting how the higher spin theory is embedded into string theory
Summary
It was shown in [23] that the N = 2 superconformal cosets that appear in the duality to the N = 2 supersymmetric higher spin theory on AdS3 can be expressed as a continuous orbifold of a free field theory in the limit where the level k → ∞. The continuous orbifold describes the theory of N free complex bosons and fermions transforming in the fundamental (and anti-fundamental) representation of U(N ). It can be represented as the orbifold (T2)N /U(N ).. Since in the N = 2 case the theory in question only involves N complex bosons and fermions, we need to remove the last factor that describes the diagonal torus (which transforms as a singlet under SN+1). The twisted sectors of the symmetric orbifold will be discussed
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