  We consider a 1+1 dimensional directed continuum polymer in a Gaussian
delta-correlated space-time random potential. For this model the moments (=
replica) of the partition function, Z(x,t), can be expressed in terms of the
attractive delta-Bose gas on the line. Based on a recent study of the structure
of the eigenfunctions, we compute the generating function for Z(x_1,t),
Z(x_2,t) under a particular decoupling assumption and thereby extend recent
results on the one-point generating function of the free energy to two points.
It is established that in the long time limit the fluctuations of the free
energy are governed by the two-point distribution of the Airy process, which
further supports that the long time behavior of the KPZ equation is the same as
derived previously for lattice growth models.
