The Topological Cp¹ Model and the Large-N Matrix Integral

We discuss the topological CP 1 model which consists of the holomorphic maps from Riemann surfaces onto CP 1 . We construct a large-N matrix model which reproduces precisely the partition function of the CP 1 model at all genera of Riemann surfaces. The action of our matrix model has the form [Formula: see text] where M is an N × N Hermitian matrix and t n,P (t n,Q ), (n = 0, 1, 2, …) are the coupling constants of the nth descendant of the puncture (Kähler) operator.