UNITARY MATRIX INTEGRALS IN THE FRAMEWORK OF THE GENERALIZED KONTSEVICH MODEL

We advocate a new approach to the study of unitary matrix models in ex ternal fields which emphasizes their relationship to generalized Konts evich models (GKM's) with nonpolynomial potentials. For example, we sh ow that the partition function of the Brezin-Gross-Witten model (BGWM) , which is defined as an integral over unitary N x N matrices, integra l[dU]e(Tr(J dagger U+JU dagger)), can also be considered as a GKM with potential V(X) = 1/X. Moreover, it can be interpreted as the generati ng functional for correlators in the Penner model. The strong and weak coupling phases of the BGWM are identified with the ''character'' (we ak coupling) and ''Kontsevich'' (strong coupling) phases of the GKM, r espectively. This type of GKM deserves classification as a p = -2 mode l (i.e. c = 28 or c = -2) when in the Kontsevich phase. This approach allows us to further identify the Harish-Chandra-Itzykson-Zuber integr al with a peculiar GKM, which arises in the study of c = 1, theory, an d, further, with a conventional two-matrix model which is rewritten in Miwa coordinates. Some further extensions of the GKM treatment which are inspired by the unitary matrix models which we have considered are also developed. In particular, as a by-product, a new, simple method of fixing the Ward identities for matrix models in an external field i s presented.