Higher spins in the symmetric orbifold of K3

Abstract

The symmetric orbifold of K3 is believed to be the CFT dual of string theory on AdS 3 × S 3 × K3 at the tensionless point. For the case when the K3 is described by the orbifold T 4 /Z 2 , we identify a subsector of the symmetric orbifold theory that is dual to a higher spin theory on AdS 3 . We analyse how the BPS spectrum of string theory can be described from the higher spin perspective, and determine which single-particle BPS states are accounted for by the perturbative higher spin theory.

The AdS3× S3× S3× S1worldsheetSmatrix

“…It would be interesting to see if the AdS integrability results already known for this background can shed some light on the dual CFT 2 . The AdS 3 /CFT 2 correspondence has been recently investigated in the higher-spin limit (see [104][105][106] and references therein). It was found that in this context the α → 0 limit provided valuable information about the theories, much as it had done in [32,42].…”

The operator product expansion between the 16 lowest higher spin currents in the $$\mathcal{N}=4$$ N = 4 superspace

“…Recently, in [6], the zeromode eigenvalue equations (and the corresponding threepoint functions) of the bosonic (higher spin) currents of spins s = 1, 2, 3 with two scalars for any finite N and k (and for large N 't Hooft limit) were obtained. (Recall that the group 1 In the large-level limit of type IIB string theory on AdS 3 ×S 3 ×S 3 ×S 1 , one of the two three-spheres becomes flat and decompactifies to R 3 (and to the three-torus T 3 ) and then one obtains type IIB string theory on AdS 3 × S 3 × T 4 . In [2], a better understanding of string theory in the tensionless limit was described from the viewpoint of Vasiliev higher spin theory.…”

Even spin N = 4 $$ \mathcal{N}=4 $$ holography

“…Note that the results of [48], regarding the symmetric product of K3 at the point K3 ∼ = T 4 /Z 2 , can also be expressed in terms of the representations of the untwisted sector of the Sp(2N ) vector model. It is argued in [48] that instead of W N =4 ∞ [0] one must consider the subalgebra obtained by removing the four singlet bosons and fermions.…”

“…The bilinear basic invariants remain, but the singlet fields are left out. Using the notation of [48], the decomposition of the single particle generators of the untwisted sector of the symmetric product of K3 in terms of Sp(2N ) representations can be found to be…”

“…It is argued in [48] that instead of W N =4 ∞ [0] one must consider the subalgebra obtained by removing the four singlet bosons and fermions. This is due to the fact that Z 2 acts by exchanging the sign of the fundamental fields, so that all states of the vector model built using an odd number of fields are projected out.…”