States and curves of five-dimensional gauged supergravity

We consider the sector of N = 8 five-dimensional gauged supergravity with n ontrivial scalar fields in the coset space SL(6,R)/SO(6), plus the metric. We find that the most general supersymmetric solution is parametrized by si x real moduli and analyze its properties using the theory of algebraic curv es. In the generic case, where no continuous subgroup of the original SO(6) symmetry remains unbroken, the algebraic curve of the corresponding soluti on is a Riemann surface of genus seven. When some cycles shrink to zero siz e the symmetry group is enhanced, whereas the genus of the Riemann surface is lowered accordingly. The uniformization of the curves is carried out exp licitly and yields various supersymmetric configurations in terms of ellipt ic functions. We also analyze the ten-dimensional type-IIB supergravity ori gin of our solutions and show that they represent the gravitational field o f a large number of D3-branes continuously distributed on hyper-surfaces em bedded in the six-dimensional space transverse to the branes. The spectra o f massless scalar and graviton excitations are also studied on these backgr ounds by casting the associated differential equations into Schrodinger equ ations with nontrivial potentials. The potentials an found to be of Caloger o type, rational or elliptic, depending on the background configuration tha t is used. (C) 2000 Elsevier Science B.V. All rights reserved.