Higher spins & strings

It is natural to believe that the free symmetric product orbifold CFT is dual to the tensionless limit of string theory on AdS 3 × S 3 × T 4 $$ {\mathbb{T}}^4 $$ . At this point in moduli space, string theory is expected to contain a Vasiliev higher spin theory as a subsector. We confirm this picture explicitly by showing that the large level limit of the N $$ \mathcal{N} $$ =4 cosets of arXiv:1305.4181, that are dual to a higher spin theory on AdS 3 , indeed describe a closed subsector of the symmetric product orbifold. Furthermore, we reorganise the full partition function of the symmetric product orbifold in terms of representations of the higher spin algebra (or rather its W ∞ $$ {\mathcal{W}}_{\infty } $$ extension). In particular, the unbroken stringy symmetries of the tensionless limit are captured by a large chiral algebra which we can describe explicitly in terms of an infinite sum of W ∞ $$ {\mathcal{W}}_{\infty } $$ representations, thereby exhibiting a vast extension of the conventional higher spin symmetry