Even spin minimal model holography

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The even spin Wᵉ∞ algebra that is generated by the stress energy tensor together with one Virasoro primary field for every even spin s ≥ 4 is analysed systematically by studying the constraints coming from the Jacobi identities. It is found that the algebra is characterised, in addition to the central charge, by one free parameter that can be identified with the self-coupling constant of the spin 4 field. We show that Wᵉ∞ can be thought of as the quantisation of the asymptotic symmetry algebra of the even higher spin theory on AdS₃. On the other hand, Wᵉ∞ is also quantum equivalent to the so(N) coset algebras, and thus our result establishes an important aspect of the even spin minimal model holography conjecture. The quantum equivalence holds actually at finite central charge, and hence opens the way towards understanding the duality beyond the leading 't Hooft limit.