We show that the 2d Poisson Sigma Model on a Poisson groupoid arises as an
effective theory of the 3d Courant Sigma Model associated to the double of the
underlying Lie bialgebroid. This field-theoretic result follows from a
Lie-theoretic one involving a coisotropic reduction of the odd cotangent bundle
by a generalized space of algebroid paths. We also provide several examples,
including the case of symplectic groupoids in which we relate the symplectic
realization construction of Crainic-Marcut to a particular gauge fixing of the
3d theory.
