Even spin minimal model holography

TL;DR

We construct and constrain the even-spin W∞^e(γ) algebra via Jacobi identities, showing it is fixed by the central charge and a single self-coupling parameter γ, and identify its wedge (classical) limit with hs^e[μ]. By formulating two quantum Drinfeld–Sokolov reductions, WB∞[μ] and WC∞[μ], the work reveals Langlands-dual and non-simply-laced structure, and establishes precise finite-N/K equivalences to SO coset algebras, thereby confirming key aspects of even-spin minimal model holography. The analysis also clarifies the spectrum, minimal representations, and the perturbative vs non-perturbative nature of bulk scalars, and shows how various coset and orbifold constructions realize the same W∞^e framework, including level-rank dualities. These results extend holographic correspondences beyond leading ’t Hooft limits and offer a concrete quantum-algebraic foundation for even-spin AdS3 holography, with implications for bulk quantisation and modular invariants.

Abstract

The even spin W^e_\infty algebra that is generated by the stress energy tensor together with one Virasoro primary field for every even spin s \geq 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 W^e_\infty can be thought of as the quantisation of the asymptotic symmetry algebra of the even higher spin theory on AdS_3. On the other hand, W^e_\infty 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.