  We study the statics and dynamics of an elastic manifold in a disordered
medium with quenched defects correlated as r^{-a} for large separation r. We
derive the functional renormalization-group equations to one-loop order, which
allow us to describe the universal properties of the system in equilibrium and
at the depinning transition. Using a double epsilon=4-d and delta=4-a
expansion, we compute the fixed points characterizing different universality
classes and analyze their regions of stability. The long-range
disorder-correlator remains analytic but generates short-range disorder whose
correlator exhibits the usual cusp. The critical exponents and universal
amplitudes are computed to first order in epsilon and delta at the fixed
points. At depinning, a velocity-versus-force exponent beta larger than unity
can occur. We discuss possible realizations using extended defects.
