Vacua of N=10 three-dimensional gauged supergravity

We study scalar potentials and the corresponding vacua of N = 10 three-dimensional gauged supergravity. The theory contains 32 scalar fields parametrizing the exceptional coset space E(6(-14))/SO(10) x U(1). The admissible gauge groups considered in this work involve both compact and non-compact gauge groups which are maximal subgroups of SO(10) x U(1) and E(6(-14)), respectively. These gauge groups are given by SO(p) x SO(10 - p) x U(1) for p = 6, ... , 10, SO(5) x SO(5), SU(4, 2) x SU(2), G(2(-14)) x SU(2, 1) and F(4(-20)). We find many AdS(3) critical points with various unbroken gauge symmetries. The relevant background isometries associated with the maximally supersymmetric critical points at which all scalars vanish are also given. These correspond to the superconformal symmetries of the dual conformal field theories in two dimensions.