Background harmonic superfields in \(N=2\) supergravity (Q1274141)

The author considers the problem of background supersymmetry in the harmonic formalism for \(D=4\) \(N=2\) supergravity (SG\(^{N=2}_{D=4}\)) in the superfield approach. Such a background supersymmetry emerges in the perturbation expansion of the SG\(^{N=2}_{D=4}\) action in powers of the gravitational constant. Imposition of the covariance with respect to this supersymmetry enables the author to give solutions of the harmonic constraints in the SG\(^{N=2}_{D=4}\). Moreover, using harmonic formalism he constructs iteratively the superfield action of the theory (where the leading term is the quadratic action of the linearized theory). Finally, it is suggested how the method considered in the paper can be used for the superfield quantization of \(N=2\) supergravity in the flat background superspace.