  We initiate the systematic construction of gauged matter-coupled supergravity
theories in two dimensions. Subgroups of the affine global symmetry group of
toroidally compactified supergravity can be gauged by coupling vector fields
with minimal couplings and a particular topological term. The gauge groups
typically include hidden symmetries that are not among the target-space
isometries of the ungauged theory. The possible gaugings are described
group-theoretically in terms of a constant embedding tensor subject to a number
of constraints which parametrizes the different theories and entirely encodes
the gauged Lagrangian.
  The prime example is the bosonic sector of the maximally supersymmetric
theory whose ungauged version admits an affine E_9 global symmetry algebra. The
various parameters (related to higher-dimensional p-form fluxes, geometric and
non-geometric fluxes, etc.) which characterize the possible gaugings, combine
into an embedding tensor transforming in the basic representation of E_9. This
yields an infinite-dimensional class of maximally supersymmetric theories in
two dimensions. We work out and discuss several examples of higher-dimensional
origin which can be systematically analyzed using the different gradings of
E_9.
