Massless Higher Spins and Holography

TL;DR

The paper investigates how free large-N SCFTs can holographically dual massless higher spin gauge theories in AdS spaces across D=4,5,7. It develops a cohesive HS framework built from singleton representations, constructs master fields, and demonstrates (where possible) consistent truncation to massless HS sectors, linking bulk amplitudes to boundary bilinear operators via 1/N expansions. It also analyzes symmetry breaking (Higgsing) of HS algebras in AdS5×S5 and AdS4×S7, explores rotating membrane solutions in AdS7, and discusses the implications for Type IIB string and M-theory in various AdS backgrounds. The work outlines how a tensionless/string/M-theory limit may realize unbroken HS phases, proposes tests via crossing-symmetric correlators, and identifies key open questions, including fully constructing interacting HS theories in 5D and 7D and understanding HS-Higgs couplings and their bulk realizations.

Abstract

We treat free large N superconformal field theories as holographic duals of higher spin (HS) gauge theories expanded around AdS spacetime with radius R. The HS gauge theories contain massless and light massive AdS fields. The HS current correlators are written in a crossing symmetric form including only exchange of other HS currents. This and other arguments point to the existence of a consistent truncation to massless HS fields. A survey of massless HS theories with 32 supersymmetries in D=4,5,7 (where the 7D results are new) is given and the corresponding composite operators are discussed. In the case of AdS_4, the cubic couplings of a minimal bosonic massless HS gauge theory are described. We examine high energy/small tension limits giving rise to massless HS fields in the Type IIB string on AdS_5 x S^5 and M theory on AdS_{4/7} x S^{7/4}. We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS_5 x S^5 and AdS_4 x S^7 where the HS symmetry is broken by finite g_{YM}. In AdS_5 x S^5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g_{YM}=0 corresponds to a critical string tension of order 1/R^2 and a finite string coupling of order 1/N. In AdS_7 x S^4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the A_{N-1}(2,0) SCFT, expandable in terms of operators with anomalous dimensions that are asymptotically small for large spin. The minimal energy configurations have semi-classical energy E=s for all s and the geometry of infinitely stretched strings with energy and spin density concentrated at the endpoints.