  We consider the type IIB Green-Schwarz superstring theory on AdS(2)xS(2)xT(6)
supported by homogeneous Ramond-Ramond 5-form flux and its type IIA T-duals.
One motivation is to understand the solution of this theory based on
integrability. This background is a limit of a 1/4 supersymmetric supergravity
solution describing four intersecting D3-branes and represents a consistent
embedding of AdS(2)xS(2) into critical superstring theory. Its AdS(2)xS(2) part
with corresponding fermions can be described by a classically integrable
PSU(1,1|2)/SO(1,1)xU(1) supercoset sigma-model.
  We point out that since the RR 5-form field has non-zero components along the
6-torus directions one cannot, in general, factorize the 10d superstring theory
into the supercoset part plus 6 bosons and 6 additional massless fermions.
Still, we demonstrate that the full superstring model (i) is classically
integrable, at least to quadratic order in fermions, and (ii) admits a
consistent classical truncation to the supercoset part. Following the analogy
with other integrable backgrounds and starting with the finite-gap equations of
the PSU(1,1|2)/SO(1,1)xU(1) supercoset we propose a set of asymptotic Bethe
ansatz equations for a subset of the quantum string states.
