Minimal local Lagrangians for higher-spin geometry

The Fronsdal Lagrangians for free totally symmetric rank-s tensors rho(mu 1...mu S) rest on suitable trace constraints for their gauge parameters and gauge fields. Only when these constraints are removed, however, the resulting equations reflect the expected free higher-spin geometry. We show that geometric equations, in both their local and non-local forms, can be simply recovered from local Lagrangians with only two additional fields, a rank-(s - 3) compensator alpha(mu 1...mu s-3) and a rank-(s - 4) Lagrange multiplier beta(mu 1...mu S-4.) In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors psi(mu 1...mu n) can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n - 2) compensator xi(mu 1...mu n-2) and a rank-(n - 3) Lagrange multiplier lambda(mu 1...mu n-3). (c) 2005 Elsevier B.V. All rights reserved.