Related papers: Isomonodromic Properties of the Seiberg-Witten Sol…
We carefully study the global structure of the solution of the $N=2$ supersymmetric pure Yang-Mills theory with gauge group $SU(2)$ obtained by Seiberg and Witten. We exploit its ${\bf Z}_2$-symmetry and describe the curve in moduli space…
We hypothesize that the vacuum is spontaneously shifted from the self-dual point in the moduli space, at which all dimensions are compact, and that the true vacuum results from the decompactification of the four space-time dimensions and…
We present unique solutions of the Seiberg-Witten Monopole Equations in which the U(1) curvature is covariantly constant, the monopole Weyl spinor consists of a single constant component, and the 4-manifold is a product of two Riemann…
The one-instanton contribution to the prepotential for N=2 supersymmetric gauge theories with classical groups exhibits a universality of form. We extrapolate the observed regularity to SU(N) gauge theory with two antisymmetric…
An introduction to Seiberg-Witten theory and its relation to theories which include gravity.
In these lectures we explain the intimate relationship between modular invariants in conformal field theory and braided subfactors in operator algebras. A subfactor with a braiding determines a matrix $Z$ which is obtained as a coupling…
The self-dual Einstein equations on a compact Riemannian 4-manifold can be expressed as a quadratic condition on the curvature of an $SU(2)$ (spin) connection which is a covariant generalization of the self-dual Yang-Mills equations. Local…
In addition to superconformal symmetry, (1,1) supersymmetric two-dimensional sigma models on special holonomy manifolds have extra symmetries that are in one-to-one correspondence with the covariantly constant forms on these manifolds. The…
We study the non-perturbative properties of N=2 super conformal field theories in four dimensions using localization techniques. In particular we consider SU(2) gauge theories, deformed by a generic epsilon-background, with four fundamental…
We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the…
A popular way to study N=1 supersymmetric gauge theories is to realize them geometrically in string theory, as suspended brane constructions, D-branes wrapping cycles in Calabi-Yau manifolds, orbifolds, and otherwise. Among the applications…
We study the path integral of a twisted $N=2$ supersymmetric Yang-Mills theory coupled with hypermultiplet having the bare mass. We explicitly compute the topological correlation functions for the $SU(2)$ theory on a compact oriented simply…
Kutasov--type duals of supersymmetric gauge theories had been studied only in the dual regime and the s-confining case. Here we extend the discussion to the case of less flavor, analogous to the case of quantum-modified moduli space in…
For a compact spinc manifold $X$ with boundary $b_1(\partial X)=0$, we consider moduli spaces of solutions to the Seiberg-Witten equations in a generalized double Coulomb slice in $L^2_1$ (i.e., $W^{1,2}$) Sobolev regularity. We prove they…
It has been shown that membranes and fivebranes are wave-like or monopole-like solutions in some higher dimensional theory. Here the picture is completed by combining the wave and monopole solutions into a single solution of Exceptional…
We study the quantum moduli spaces and dynamical superpotentials of four dimensional $SU(2)^r$ linear and ring moose theories with $\mathcal{N}=1$ supersymmetry and link chiral superfields in the fundamental representation. Nontrivial…
We consider type IIA brane configurations, similar to those that realize SO(2N) supersymmetric QCD, that include orientifold planes and anti-branes. Such brane configurations lead to Sp(2N) field theories that become supersymmetric in the…
We introduce and study equivariant Seiberg-Witten invariants for $4$-manifolds equipped with a smooth action of a finite group $G$. Our invariants come in two types: cohomological, valued in the group cohomology of $G$ and $K$-theoretic,…
We study brane configurations which correspond to field theories in four dimension with N=2 and N=1 supersymmetry. In particular we discuss brane motions that translate to Seiberg's duality in N=1 models recently studied by Elitzur, Giveon…
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…