Infinite Symmetry Algebras of Extended Supergravity Theories

When extended supergravity theories with noncompact symmetry groups are written in a physical gauge, the noncompact symmetries join with the supersymmetries to generate an infinitedimensional algebra. The details are worked out explicitly for a two-dimensional theory with an SU(1,1) internal symmetry. Our analysis confirms the observation of Elfis et al. that the infinite rigid superalgebra should be obtained from the finite-dimensional local superalgebra by replacing scalar fields with their asymptotic values at infinity. The infinite algebra is described by extending the super-Poincar6 generators to functions on the coset space defined by the scalar fields at infinity. While mathematically nontrivial, this result is, in a certain sense, trivial from a physical point of view.