Coupling supersymmetric nonlinear sigma models to supergravity

Abstract

It is known that supersymmetric nonlinear sigma models for the compact Kähler manifolds G/H cannot be consistently coupled to supergravity, since the Kähler potentials are not invariant under G transformation. We show that the supersymmetric nonlinear sigma models can be deformed such that the Kähler potential becomes exactly G-invariant if and only if one enlarges the manifolds by dropping all the U(1)'s in the unbroken subgroup H. Then, those nonlinear sigma models can be coupled to supergravity without losing the G invariance.