Local Supersymmetry and Gravitation
We discuss a recently1,2,3 discovered Lagrangian field theory for gravitation, which is locally supersymmetric (“super-gravity”) and which uses normal four dimensional spacetime instead of superspace. The action contains the Einstein action and the minimally coupled spin 3/2 action together with a non-derivative four-fermion interaction of gravitational strength. When recast in a first order formalism with torsion, the action contains no four-fermion term but the spin 3/2 field is coupled in a non-minimal way.
The commutator of two local supersymmetry transformations produces a general coordinate and local Lorentz transformation. This deeper symmetry which connects the structure of spacetime with transformations between bosons and fermions, seems interesting. Applications to quantum gravity are discussed.
KeywordsGauge Theory Gauge Field Supersymmetry Transformation Dirac Matrice Auxiliary Field
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