Comments on higher-spin holography

TL;DR

This paper reviews the conjectured holographic duality between vector models with quartic interactions and higher-spin theories, discussing its extensions and the implications of higher spin symmetries on quantum corrections.

Contribution

It explores the conjecture's validity beyond the large-N limit and in various generalizations, emphasizing the role of higher spin symmetries in bulk quantum corrections.

Findings

The duality holds for any number of scalar fields and coupling constants under certain conditions.

Higher spin symmetries may prevent quantum corrections in the bulk.

Extensions to higher dimensions and beyond the singlet sector are discussed.

Abstract

The conjectured holographic duality between vector models with quartic interaction and higher-spin field theory in the bulk is reviewed, with emphasis on some versions and generalisations (higher dimensions, beyond the singlet sector, etc) which have not been much investigated yet. The strongest form of the conjecture assumes that it holds for any (not necessarily large) number of massless scalar fields and for any value of the coupling constant. Since the quartic interaction is of double-trace type, the exact duality (for any value of the coupling constant) automatically follows from its validity at the Gaussian fixed point (for vanishing coupling constant). The validity of the latter also implies that unbroken higher spin symmetries should prevent quantum corrections in the bulk.