Abstract
The symmetries of string theory on ${\rm AdS}_3 \times {\rm S}^3 \times \mathbb{T}^4$ at the dual of the symmetric product orbifold point are described by a so-called Higher Spin Square (HSS). We show that the massive string spectrum in this background organises itself in terms of representations of this HSS, just as the matter in a conventional higher spin theory does so in terms of representations of the higher spin algebra. In particular, the entire untwisted sector of the orbifold can be viewed as the Fock space built out of the multiparticle states of a single representation of the HSS, the so-called `minimal' representation. The states in the twisted sector can be described in terms of tensor products of a novel family of representations that are somewhat larger than the minimal one.
Highlights
Through gauge-string dualities we can access other backgrounds which show enhanced unbroken symmetries
In [14], we showed that these single particle currents, which generate the unbroken symmetry algebra, have a rather novel underlying structure — which we dubbed as the Higher Spin Square (HSS)
The relevant higher spin symmetry algebra is the Higher Spin Square (HSS), and the full spectrum can be organised in terms of representations of this algebra
Summary
Let us begin by reviewing the structure of the unbroken stringy symmetry algebra of the AdS3×S3×T4 background at the point in moduli space described by the symmetric product orbifold (T4)N /SN. This turned out to be possible, essentially because of the presence of an additional, less obvious, higher spin symmetry This is best illustrated for the case of the chiral algebra of a single complex boson (rather than the full T4 theory), and we shall in this paper, often restrict to this case for simplicity. These additional representations, labelled by the pairs (n, m), need to be added to the higher spin algebra hs[1] to generate the bosonic analogue of the stringy symmetry algebra. The monomials of the form (∂φ1,2)n (together with lower order correction terms) can be written in terms of neutral bilinears of the corresponding complex fermion, i.e., as bilinear U(1) × U(1) singlets These bilinears in turn generate another higher spin algebra, whose wedge algebra consists of two copies of hs[0] (with asymptotic extension W1+∞[0]). Most of the discussion in the rest of the paper does not rely directly on this construction; readers who want to go directly to the discussion of the matter sector and its representation content from the point of view of the HSS may skip the remainder of this section
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
