Abstract
For the proposed duality relating a family of N=4 superconformal coset models to a certain supersymmetric higher spin theory on AdS_3, the asymptotic symmetry algebra of the bulk description is determined. It is shown that, depending on the choice of the boundary charges, one may obtain either the linear or the non-linear superconformal algebra on the boundary. We compare the non-linear version of the asymptotic symmetry algebra with the non-linear coset algebra and find non-trivial agreement in the 't Hooft limit, thus giving strong support for the proposed duality. As a by-product of our analysis we also show that the W_infinity symmetry of the coset theory is broken under the exactly marginal perturbation that preserves the N=4 superconformal algebra.
Highlights
Symmetries of higher spin theories on AdS3 [19, 20], see [21, 22] for subsequent developments
As a by-product of our analysis we show that the W∞ symmetry of the coset theory is broken under the exactly marginal perturbation that preserves the N = 4 superconformal algebra
One may expect that the dual of the higher spin theory should lead to the non-linear version Aγ of the large N = 4 superconformal algebra [25]; this misses the u(1) generator that corresponds to the S1 of the putative string target space, and it is at odds with the observation that the supergravity spectrum organises itself into representations of the linear Aγ algebra [38], suggesting that the dual CFT should have this symmetry
Summary
Particular, the non-linear Aγ N = 4 superconformal algebra as was already anticipated in [25] This algebra is the natural asymptotic symmetry algebra associated to the subalgebra D(2, 1|α) ⊂ shs2[λ]. With similar expressions for the remaining generators These OPEs agree precisely with those of the non-linear Aγ algebra, as given for example in appendix B.3 of [25], provided we identify kcs k+k− k+ + k−. The lowest non-trivial multiplet (denoted by R(1) in that paper) is generated from a Virasoro primary operator of spin 1 that transforms in a singlet representation under su(2) ⊕ su(2) We shall denote it by V (1)0 in the following, and introduce for the superdescendants the notation fields h (l+, l−) multiplet. We shall explain there that the truncation patterns of the asymptotic symmetry algebra (to which we turn) are nicely reproduced by the dual CFT
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