  We use a version of the Skorokhod integral to give a simple and rigorous
formulation of the Wick-ordered (stochastic) heat equation with planar white
noise, representing the free energy of an undirected random polymer. The
solution for all times is expressed as the L1 limit of a martingale given by
the Feyman-Kac formula and defines a randomized shift, or Gaussian
multiplicative chaos. The fluctuations far from the centre are shown to be
given by the one-dimensional KPZ equation.
