Abstract :
We present an elementary and detailed analysis of the Penner model with operators inserted. From a general point of view, correlation functions and loop amplitudes of this model may be related to each other by means of the dual transformation of Feynman diagrams. Such a relationship is shown to manifest the duality symmetry under t →- t−1 and N → Nt, after suppressing a quadratic term in the matrix model potential defined on the dual lattice. It is argued that this term is immaterial at the critical point tc = -1, thus permitting to give an explicit description of the macroscopic loops via the determination of correlators. We carry out the nonperturbative construction of all such correlators in concrete terms, compute their large-N expansions and define the continuum limit. Some applications are also discussed, among which is a comparison between the n-point function of the Penner model and that of c = 1 strings.
