Massless higher spins and holography

Abstract

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 × S 5 and M-theory on AdS 4/7 × S 7/4 . We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS 5 × S 5 and AdS 4 × S 7 where the HS symmetry is broken by finite g YM . In AdS 5 × 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 2 =0 corresponds to a critical string tension of order 1/ R 2 and a finite string coupling of order 1/ N . In AdS 7 × 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.