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.
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Kumar, D., Sharma, M. Symmetry algebras of stringy cosets. J. High Energ. Phys. 2019, 179 (2019). https://doi.org/10.1007/JHEP08(2019)179
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DOI: https://doi.org/10.1007/JHEP08(2019)179