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Symmetry algebras of stringy cosets

  • Dushyant Kumar
  • Menika SharmaEmail author
Open Access
Regular Article - Theoretical Physics

Abstract

We find the symmetry algebras of cosets which are generalizations of the minimal-model cosets, of the specific form \( \frac{\mathrm{SU}{(N)}_k\times \mathrm{SU}{(N)}_{\mathrm{\ell}}}{\mathrm{SU}{(N)}_{k+\mathrm{\ell}}} \). We study this coset in its free field limit, with k, ℓ → ∞, where it reduces to a theory of free bosons. We show that, in this limit and at large N, the algebra \( {\mathcal{W}}_{\infty}^e\left[1\right] \) emerges as a sub-algebra of the coset algebra. The full coset algebra is a larger algebra than conventional \( \mathcal{W} \)-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.

Keywords

Conformal and W Symmetry Higher Spin Symmetry AdS-CFT Correspondence 

Notes

Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited

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Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Harish-Chandra Research InstituteAllahabadIndia
  2. 2.Department of Mathematics, CityUniversity of LondonLondonU.K.

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