Higher Spin Holography, RG, and the Light Cone

TL;DR

Mintun and Polchinski investigate whether a sharp AdS radial cutoff can be extracted from the RG of the dual CFT in the higher-spin/vector model context. They show that a cutoff on bilinears is necessary to obtain local bulk dynamics at linear order and demonstrate, in the light-cone frame, that the bilocal RG reproduces the Fronsdal equations with a precise bulk–boundary dictionary and a link to the precursor construction. The work provides detailed light-cone GKPW mappings and a gauge-invariant Weyl-curvature dictionary, clarifying how boundary bilocals encode bulk higher-spin fields. Covariant RG and bulk interactions, however, remain as open challenges requiring further development and synthesis with other holographic frameworks.

Abstract

We revisit the derivation of higher spin bulk theory using the renormalization group in the dual field theory. We argue that existing proposals have problems already at the level of linearized perturbations on AdS. This is due to the form of the cutoff, which must act on bilinears in the fundamental fields rather than on the fields themselves. For the light-cone collective field theory, we show that the RG produces the correct linearized perturbations. We relate this to the precursor formula of de Mello Koch, Jevicki, Jin and Rodrigues, and we also elaborate on that result. The covariant RG and bulk interactions remain problems for the future.