Abstract
We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold SymN(T4) to all orders in N. This allows us to compute how 1/4-BPS states of the D1-D5 system on AdS3 × S3 × T4 are lifted as we move away from the orbifold point. As an application we confirm a previous observation that in the large N limit not all 1/4-BPS states that can be lifted do get lifted. This provides evidence that the supersymmetric index actually undercounts the number of 1/4-BPS states at a generic point in the moduli space.
Highlights
(see [2,3,4] for an exact duality between the symmetric orbifold and a tensionless string with one unit of NS-NS flux when X = T 4 and SymN (T 4))
We establish a framework for doing second order conformal perturbation theory for the symmetric orbifold SymN (T 4) to all orders in N
As an application we confirm a previous observation that in the large N limit not all 1/4-BPS states that can be lifted do get lifted. This provides evidence that the supersymmetric index undercounts the number of 1/4-BPS states at a generic point in the moduli space
Summary
Let us briefly discuss how our results fit in with the literature on conformal perturbation theory for holographic CFTs. [35] computed the lifting of single trace chiral states, that is higher spin fields with h = s and h = 0 They restricted to states which are uncharged with respect to the large N = 4 SCA. We perform our computations in the NS sector, but the results are directly related by spectral flow The triplet they consider corresponds again to our flavor currents J, and we find that they all get lifted by an equal amount. In a series of papers [38,39,40,41,42] lifting of various twisted sector Ramond fields and some of their composite operators are computed up to second order in perturbation theory. An ancillary Mathematica notebook, lifting.nb, in the supplementary material, performs the computation of lifting at the second order in perturbation theory
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