Massless higher spins and holography
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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 AdS4, 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 AdS5 S5 and M-theory on AdS4/7 S7/4. We discuss breaking of HS symmetries to the symmetries of ordinary supergravity, and a particularly natural Higgs mechanism in AdS5 S5 and AdS4 S7 where the HS symmetry is broken by finite gYM. In AdS5 S5 it is shown that the supermultiplets of the leading Regge trajectory cross over into the massless HS spectrum. We propose that g2YM = 0 corresponds to a critical string tension of order 1/R2 and a finite string coupling of order 1/N. In AdS7 S4 we give a rotating membrane solution coupling to the massless HS currents, and describe these as limits of Wilson surfaces in the AN-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. 2002 Elsevier Science B.V. All rights reserved.
