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We search for $N=2$, $d=4$ theories which can be realized both as heterotic string compactifications on $K_{3}\times T^{2}$ and as type II string compactifications on Calabi-Yau threefolds. In such cases, the exact non-perturbative…

It was recently argued by Nguyen-Tanizaki-Unsal that two-dimensional pure Yang-Mills theory is equivalent to (decomposes into) a disjoint union of (invertible) quantum field theories, known as universes. In this paper we compare this…

By constructing a nilpotent extended BRST operator $\bs$ that involves the N=2 global supersymmetry transformations of one chirality, we show that the standard N=2 off-shell Super Yang Mills Action can be represented as an exact BRST term…

In these lectures we discuss various aspects of gauge theories with extended $N=2$ and $N=4$ supersymmetry that are at the basis of recently found exact results. These results include the exact calculation of the low energy effective action…

Continuous dual symmetry in electrodynamics, Yang-Mills theory and gravitation is investigated. Dual invariant which leads to badly nonlinear motion equations is chosen as a Lagrangian of the pure classical dual nonlinear electrodynamics.…

We derive the four dimensional N=1/2 super Yang-Mills theory from tree-level computations in RNS open string theory with insertions of closed string Ramond-Ramond vertices. We also study instanton configurations in this gauge theory and…

We discuss the N=2 SU(2) Yang-Mills theory coupled with a massive matter in the weak coupling. In particular, we obtain the instanton expansion of its prepotential. Instanton contributions in the mass-less limit are completely reproduced.…

We propose a discretization of two dimensional Euclidean Yang-Mills theories with N=2 supersymmetry which preserves exactly both gauge invariance and an element of supersymmetry. The approach starts from the twisted form of the continuum…

{}~~~We show that the recently constructed $~N=4$~ supersymmetric self-dual Yang-Mills theory as the consistent background of \hbox{$~N=2$} open superstring will generate Witten's topological field theory in two-dimensions as a descendant…

Taking the N=2 strings as the starting point, we discuss the equivalent self-dual field theories and analyse their symmetry structure in 2+2 dimensions. Restoring the full `Lorentz' invariance in the target space necessarily leads to an…

It is argued that there are strong similarities between the infra-red physics of N=2 supersymmetric Yang-Mills and that of the quantum Hall effect, both systems exhibit a hierarchy of vacua with a sub-group of the modular group mapping…

We write down all orders large $N$ expansions for the dimensions of irreducible representations of $O(N)$ and $Sp(N)$. We interpret all the terms in these expansions as symmetry factors for singular worldsheet configurations, involving…

Three-dimensional Yang-Mills theory allows for a deformation quadratic in the field strengths which can not be integrated to a local action without auxiliary fields. Yet, its covariant divergence consistently vanishes after iterating the…

In this paper we consider features of graviton scattering in Matrix theory compactified on a 2-torus. The features which interest us can only be determined by nonperturbative effects in the corresponding 2+1 dimensional super Yang Mills…

N=2 supersymmetric Yang--Mills theories coupled to matter are considered in the Wess--Zumino gauge. The supersymmetries are realized nonlinearly and the anticommutator between two susy charges gives, in addition to translations, gauge…

In this paper we explicitly obtain the leading corrections to the SU(N) N=2 prepotential due to stringy instantons both in flat space-time and in the presence of a non-trivial graviphoton background field. We show that the stringy…

We give a proof by direct computation that at tree level, the twistor-like superstring theory in the pure spinor formalism proposed very recently by Berkovits describes ten-dimensional N=1 super Yang-Mills in its heterotic version, and type…

We show that the $N=2$ and $N=4$ SUSY Yang-Mills action can be reformulated in the sense of non-commutative geometry on $M^4\times (Z_2\oplus Z_2)$ in a rather simple way. In this way the scalars or pseudoscalars are viewed as gauge fields…

We perform the dual transformation of the Yang-Mills theory in d=3 dimensions using the Wilson action on the cubic lattice. The dual lattice is made of tetrahedra triangulating a 3-dimensional curved manifold but embedded into a flat…

Starting from a self-dual $SU(\infty)$ Yang-Mills theory in $(2+2)$ dimensions, the Plebanski second heavenly equation is obtained after a suitable dimensional reduction. The self-dual gravitational background is the cotangent space of the…