Fronsdal fields from gauge functions in Vasiliev's higher-spin gravity
Published 2019-05-15Version 1
Working within Vasiliev's theory, we construct an equivalence class of linearized gauge functions that give rise to a generating functional for unfolded free Fronsdal fields in accordance with Vasiliev's central on mass shell theorem. Using this construction, we map linearized solutions of Vasiliev's equations obtained from zero-form integration constants and vacuum gauge functions in Weyl order to Fronsdal fields on the mass shell given in normal order. We exemplify this map for massless particle and higher spin black hole modes. We also show that unfolded Fronsdal fields arise upon imposing a gauge condition on the linearized twistor space connection that is weaker than the one used in Vasiliev's original analysis of his equations. We incorporate this relaxed gauge condition into a Fefferman-Graham-like scheme for imposing asymptotically locally anti-de Sitter (ALAdS) boundary conditions on the full master fields such that the asymptotically free Fronsdal fields of the full theory are given by the linearized fields. We use this scheme to provide the Frobenius--Chern--Simons theory with a branch on which it admits a higher spin gravity interpretation.