We consider a BRST approach to G/H coset WZNW models, {\it i.e.} a formulation in which the coset is defined by a BRST condition. We will give the precise ingrediences needed for this formulation. Then we will prove the equivalence of this approach to the conventional coset formulation by solving the the BRST cohomology. This will reveal a remarkable connection between integrable representations and a class of non-integrable representations for negative levels. The latter representations are also connected to string theories based on non-compact WZNW models. The partition functions of G/H cosets are also considered. The BRST approach enables a covariant construction of these, which does not rely on the decomposition of G as $G/H\times H$. We show that for the well-studied examples of $SU(2)_k \times SU(2)_1/SU(2)_{k+1}$ and $SU(2)_k/U(1)$, we exactly reproduce the previously known results.Comment: 23 pages latex file. G\"oteborg ITP 93-01 ( Not encoded version

One-instanton predictions are obtained from the Seiberg-Witten curve derived from M-theory by Landsteiner and Lopez for the Coulomb branch of N = 2 supersymmetric SU(N) gauge theory with a matter hypermultiplet in the antisymmetric representation. Since this cubic curve describes a Riemann surface that is non-hyperelliptic, a systematic perturbation expansion about a hyperelliptic curve is developed, with a comparable expansion for the Seiberg-Witten differential. Calculation of the period integrals of the SW differential by the method of residues of D'Hoker, Krichever, and Phong enables us to compute the prepotential explicitly to one-instanton order.It is shown that the one-instanton predictions for SU(2), SU(3), and SU(4) agree with previously available results. For SU(N), N ≥ 5, our analysis provides explicit predictions of a curve derived from M-theory at the one-instanton level in field theory.

One-instanton predictions for the prepotential are obtained from the Seiberg-Witten curve for the Coulomb branch of N = 2 supersymmetric gauge theory for the product group m n=1 SU(N n ) with a massless matter hypermultiplet in the bifundamental representation (N n ,N n+1 ) of SU(N n ) × SU(N n+1 ) for n = 1 to m − 1, together with N 0 and N m+1 matter hypermultiplets in the fundamental representations of SU(N 1 ) and SU(N m ) respectively. The derivation uses a generalization of the systematic perturbation expansion about a hyperelliptic curve developed by us in earlier work.

One-instanton predictions are obtained from certain non-hyperelliptic Seiberg-Witten curves derived from M-theory for N=2 supersymmetric gauge theories. We consider SU(N 1 )×SU(N 2 ) gauge theory with a hypermultiplet in the bifundamental representation together with hypermultiplets in the defining representations of SU(N 1 ) and SU(N 2 ). We also consider SU(N) gauge theory with a hypermultiplet in the symmetric or antisymmetric representation, together with hypermultiplets in the defining representation. The systematic perturbation expansion about a hyperelliptic curve together with the judicious use of an involution map for the curve of the product groups provide the principal tools of the calculations.