Coupling Supersymmetric Nonlinear Sigma Models to Supergravity

Understand

It is known that supersymmetric nonlinear sigma models for the compact Kahler manifolds G/H cannot be consistently coupled to supergravity, since the Kahler potentials are not invariant under the G transformation.

• We show that the supersymmetric nonlinear sigma models can be deformed such that the Kahler potential be 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.