Minimal local Lagrangians for higher-spin geometry

Abstract

The Fronsdal Lagrangians for free totally symmetric rank-s tensors φμ1...μsrest 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 αμ1...μs-3 and a rank-(s - 4) Lagrange multiplier βμ1...μs-4. In a similar fashion, we show that geometric equations for unconstrained rank-n totally symmetric spinor-tensors ψμ1...μn can be simply recovered from local Lagrangians with only two additional spinor-tensors, a rank-(n - 2) compensator ξμ1...μn-2 and a rank-(n - 3) Lagrange multiplier λμ1...αn-3. © 2005 Elsevier B.V. All rights reserved.