Higher derivative supergravity is equivalent to standard supergravity coupled to matter

Abstract

We generalize a recent theorem by Whitt (the equivalence of R+ αR 2 gravity with the Einstein theory coupled to a scalar field with specified non-linear self-couplings) to N = 1 supergravity in four dimensions. Pure R + αR 2 supergravity turns out to be equivalent to standard supergravity coupled to two chiral multiplets. The corresponding Kähler metric is the same as in no-scale models, but the superpotential is different. We give also four generalizations of the above theorem: (i) we couple matter and allow the coefficient of R 2 to be field-dependent; (ii), (iii) we consider arbitrary powers of the scalar curvature R and (iv) we consider arbitrary functions of matter fields, R, □ R, □ 2 R, etc. Peculiar phenomena occur when no-scale models are coupled to higher powers of R. We present some applications of the above results, in particular in connection with superstring phenomenology.