On the Low-Energy Effective Action of N=2 Supersymmetric Yang-Mills Theory

We investigate the perturbative part of Seiberg's low-energy effective action of N=2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on $U(1)_R$ anomaly and non-perturbative $\beta$-function arguments.Comment: 27 pages, RevTex, no figure

Duality and the Legendre Transform

We define a weak-strong coupling transformation based on the Legendre transformation of the effective action. In the case of N\es 2 supersymmetric Yang-Mills theory, this coincides with the duality transform on the low energy effective action considered by Seiberg and Witten. This Legendre transform interpretation of duality generalizes directly to the full effective action, and in principle to other theories.Comment: 6 pages, LaTe

The Vacuum Structure and Spectrum of N=2 Supersymmetric SU(N) Gauge Theory

We present an exact description of the metric on the moduli space of vacua and the spectrum of massive states for four dimensional N=2 supersymmetric SU(n) gauge theories. The moduli space of quantum vacua is identified with the moduli space of a special set of genus n-1 hyperelliptic Riemann surfaces.Comment: 11 pages, Revtex, 2 figures. Reference adde

BPS partition functions in N = 4 Yang-Mills theory on T^4

We consider N = 4 Yang-Mills theory on a flat four-torus with the R-symmetry current coupled to a flat background connection. The partition function depends on the coupling constant of the theory, but when it is expanded in a power series in the R-symmetry connection around the loci at which one of the supersymmetries is unbroken, the constant and linear terms are in fact independent of the coupling constant and can be computed at weak coupling for all non-trivial 't Hooft fluxes. The case of a trivial 't Hooft flux is difficult because of infrared problems, but the corresponding terms in the partition function are uniquely determined by S-duality.Comment: 23 pages, v2 Minor correction

Tree Unitarity and Partial Wave Expansion in Noncommutative Quantum Field Theory

The validity of the tree-unitarity criterion for scattering amplitudes on the noncommutative space-time is considered, as a condition that can be used to shed light on the problem of unitarity violation in noncommutative quantum field theories when time is noncommutative. The unitarity constraints on the partial wave amplitudes in the noncommutative space-time are also derived.Comment: 15 pages, 1 figur