CALOGERO-MOSER SYSTEMS IN SU(N) SEIBERG-WITTEN THEORY

The Seiberg-Witten curve and differential for N = 2 supersymmetric SU( N) gauge theory, with a massive hypermultiplet in the adjoint represen tation of the gauge group, are analyzed in terms of the elliptic Calog ero-Moser integrable system. A new parametrization for the Calogero-Mo ser spectral curves is found, which exhibits the classical vacuum expe ctation values of the scalar field of the gauge multiplet. The one-loo p perturbative correction to the effective prepotential is evaluated e xplicitly, and found to agree with quantum field theory predictions. A renormalization group equation for the variation with respect to the coupling is derived for the effective prepotential, and may be evaluat ed in a weak-coupling series using residue methods only. This gives a simple and efficient algorithm for the instanton corrections to the ef fective prepotential to any order. The one-and two-instanton correctio ns are derived explicitly. Finally, it is shown that certain decouplin g limits yield N = 2 supersymmetric theories for simple gauge groups S U(N-1) with hypermultiplets in the fundamental representation, while o thers yield theories for product gauge groups SU(N-1) x ... x SU(N-p), with hypermultiplets in fundamental and bi-fundamental representation s, The spectral curves obtained this way for these models agree with t he ones proposed by Witten using D-branes and M-theory. (C) 1998 Elsev ier Science B.V.