Even spin minimal model holography

TL;DR

This paper systematically analyzes the even spin W^e_ algebra, revealing its structure, parameterization, and its role as the quantum symmetry algebra in even higher spin AdS_3 holography, establishing a key duality with coset models.

Contribution

It characterizes the even spin W^e_ algebra, identifies its free parameter, and demonstrates its quantum equivalence to SO(N) coset algebras, supporting the even spin minimal model holography conjecture.

Findings

W^e_ algebra is characterized by a free parameter related to the spin 4 self-coupling.

W^e_ algebra is the quantization of the asymptotic symmetry algebra of even higher spin theory on AdS_3.

W^e_ is quantum equivalent to SO(N) coset algebras at finite central charge.

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.