The higher spin rectangle

138

180

The spectrum of superstrings on AdS 3 × S 3 × M 4 with pure NS-NS flux is analysed for the background where the radius of the AdS space takes the minimal value (k = 1). Both for M 4 = S 3 × S 1 and M 4 = T 4 we show that there is a special set of physical states, coming from the bottom of the spectrally flowed continuous representations, which agree in precise detail with the single particle spectrum of a free symmetric product orbifold. For the case of AdS 3 × S 3 × T 4 this relies on making sense of the world-sheet theory at k = 1, for which we make a concrete proposal. We also comment on the implications of this striking result.

Section: Discussionmentioning

confidence: 88%

Tensionless string spectra on AdS3

Gaberdiel

Gopakumar

2018

138

180

Symmetry algebras of stringy cosets

Kumar

Sharma

2019

Self Cite

We find the symmetry algebras of cosets which are generalizations of the minimalmodel cosets, of the specific form SU (N ) k ×SU (N ). We study this coset in its free field limit, with k, → ∞, where it reduces to a theory of free bosons. We show that, in this limit and at large N , the algebra W e ∞ [1] emerges as a sub-algebra of the coset algebra. The full coset algebra is a larger algebra than conventional W-algebras, with the number of generators rising exponentially with the spin, characteristic of a stringy growth of states. We compare the coset algebra to the symmetry algebra of the large N symmetric product orbifold CFT, which is known to have a stringy symmetry algebra labelled the 'higher spin square'. We propose that the higher spin square is a sub-algebra of the symmetry algebra of our stringy coset.

Instanton R-matrix and $$ \mathcal{W} $$-symmetry

Procházka¹

2019

We study the relation between W 1+∞ algebra and Arbesfeld-Schiffmann-Tsymbaliuk Yangian using the Maulik-Okounkov R-matrix. The central object linking these two pictures is the Miura transformation. Using the results of Nazarov and Sklyanin we find an explicit formula for the mixed R-matrix acting on two Fock spaces associated to two different asymptotic directions of the affine Yangian. Using the free field representation we propose an explicit identification of Arbesfeld-Schiffmann-Tsymbaliuk generators with the generators of Maulik-Okounkov Yangian. In the last part we use the Miura transformation to give a conformal field theoretic construction of conserved quantities and ladder operators in the quantum mechanical rational and trigonometric Calogero-Sutherland models on which a vector representation of the Yangian acts.