The emergence of higher-spins in string theory from a worldsheet perspective

Abstract

The tensionless regime of string theory is exp ected to exhibit a large unbroken symmetry which is hidden at lower energies. This prosp ect has b een addressed in the context of b oth AdS4/CFT3 and AdS3/CFT2 correspondences, where the holographic dualities mediate in a manageable way the emergence of (enhanced) higher-spin symmetries. We start by extensively reviewing the AdS3/CFT2 case and isolating an even-spin subsector of string massless higher-spin states. We then organise and begin the program of understanding these emergent symmetries from a purely string-theoretic point of view. The main di culty in this program is that the dual CFT description of strings in AdS3 is located at a point in moduli space for which there is no general covariant string description. In particular, the spacetime-covariant worldsheet theory cannot accommodate for the presence of background R-R uxes without the break of locality. We therefore initiate the program at the point with pure NS-NS ux, which does admit a covariant worldsheet description as a WZW-model, while keeping the holographic results as a guideline. As expected we do not nd massless higher-spin elds at this point, except at unit level where a special class of continuous representations becomes massless. We also isolate an even-spin discrete subsector of the leading Regge trajectory, which is a suitable candidate to correspond to the previously isolated massless higher-spin elds. We then proceed to present a (partially) covariant worldsheet description away from this point, with the help of the hybrid formalism. This formalism has its own inconveniences and technical di culties, which we report in detail, and which prevent us from computing the full string spectrum. These di culties can be lifted in a large-charge limit, in which the full worldsheet spectrum is shown to reproduce the plane-wave spectrum of string theory with mixed ux. Finally, we derive some consequences for the full string spectrum from some partial computations: we retrieve a set of BPS states which were missing from the pure NS-NS spectrum, and we show that long strings become non-unitary.