Observables and Microscopic Entropy of Higher Spin Black Holes

TL;DR

This paper develops a canonical formalism for higher spin black hole thermodynamics within holographic dualities, clarifying the bulk-boundary correspondence and ensuring consistency with CFT interpretations.

Contribution

It introduces a new canonical formalism for higher spin black hole thermodynamics that differs from existing formalisms but maintains a consistent CFT interpretation.

Findings

Formalism aligns with the holomorphic approach but differs in charges and potentials.

Provides a detailed analysis for spin-2 and spin-3 cases.

Generalizes to hs[bbeta] and sl(N,R) algebras.

Abstract

In the context of recently proposed holographic dualities between higher spin theories in AdS3 and 1+1-dimensional CFTs with W-symmetry algebras, we revisit the definition of higher spin black hole thermodynamics and the dictionary between bulk fields and dual CFT operators. We build a canonical formalism based on three ingredients: a gauge-invariant definition of conserved charges and chemical potentials in the presence of higher spin black holes, a canonical definition of entropy in the bulk, and a bulk-to-boundary dictionary aligned with the asymptotic symmetry algebra. We show that our canonical formalism shares the same formal structure as the so-called holomorphic formalism, but differs in the definition of charges and chemical potentials and in the bulk-to-boundary dictionary. Most importantly, we show that it admits a consistent CFT interpretation. We discuss the spin-2 and spin-3 cases in detail and generalize our construction to theories based on the hs[\lambda] algebra, and on the sl(N,R) algebra for any choice of sl(2,R) embedding.