Open/closed topological ℂℙ¹ sigma model revisited

We consider the topological sigma-model on Riemann surfaces with genus g and h holes, and target space ℂℙ¹ ≅ S². We calculate the correlation functions of bulk and boundary operators, and study the symmetries of the model and its most general deformation. We study the open/closed topological field theory (TFT) correspondence by summing up the boundaries. We argue that this summation can be understood as a renormalization of the closed TFT. We couple the model to topological gravity and derive constitutive relations between the correlation functions of bulk and boundary operators.