  Using an extended dynamical cluster approximation we study superconductivity
in the two-dimensional t-J model. In analogy to the extended dynamical mean
field theory, non-local spin fluctuations are treated self-consistently with an
additional Bosonic bath. To solve the effective cluster problem, we employ an
extended non-crossing approximation which allows for transitions to the
symmetry-broken state. At sufficiently low temperatures we find a stable
superconducting solution with d-wave order parameter. Upon pairing, the
exchange energy is lowered, consistent with an exchange-based pairing
mechanism.
