Related papers: BPS Geodesics in N=2 Supersymmetric Yang-Mills The…
Using Seiberg-Witten theory it is known that the dynamics of N=2 supersymmetric SU(n) Yang-Mills theory is determined by a Riemann surface. In particular the mass formula for BPS states is given by the periods of a special differential on…
We show how the Riemann surface $\Sigma$ of $N=2$ Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The $3$-branes that give rise…
Conformal mapping techniques are used to determine analytically the geodesics on the Seiberg-Witten Riemann surface which correspond to the BPS dyon states in N=2 SUSY QCD with gauge group SU(2) and up to three flavors of massless…
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 show how BPS states of supersymmetric SU(2) Yang-Mills with matter -both massless and massive- are described as self-dual strings on a Riemann surface. This connection enables us to prove the stability and the strong coupling behaviour…
We present a first step towards generalizing the work of Seiberg and Witten on N=2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus $n-1$ Riemann surfaces to…
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of…
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…
After the work of Seiberg and Witten, it has been seen that the dynamics of N=2 Yang-Mills theory is governed by a Riemann surface $\Sigma$. In particular, the integral of a special differential $\lambda_{SW}$ over (a subset of) the periods…
The thermodynamics of four-dimensional SU(2) N=2 super-Yang-Mills theory is examined in both high and low temperature regimes. At low temperatures, compelling evidence is found for two distinct equilibrium states related by a spontaneously…
It was observed recently, that the low energy effective action of the four-dimensional supersymmetric theories may be obtained as a certain limit of M Theory. From this point of view, the BPS states correspond to the minimal area membranes…
We study BPS states of 5d $\mathcal{N}=1$ $SU(2)$ Yang-Mills theory on $S^1\times \mathbb{R}^4$. Geometric engineering relates these to enumerative invariants for the local Hirzebruch surface $\mathbb{F}_0$. We illustrate computations of…
We use the SU(2) 't Hooft-Polyakov monopole configuration, and its BPS version, to test the integral equations of the Yang-Mills theory. Those integral equations involve two (complex) parameters which do not appear in the differential…
We review the generalization of the work of Seiberg and Witten on N=2 supersymmetric SU(2) Yang-Mills theory to SU(n) gauge groups. The quantum moduli spaces of the effective low energy theory parametrize a special family of hyperelliptic…
We review recent work on the study of N=2 super Yang-Mills theory with gauge group SU(N) from the point of view of the Whitham hierarchy, mainly focusing on three main results: (i) We develop a new recursive method to compute the whole…
We consider duality transformations in N=2, d=4 Yang--Mills theory coupled to N=2 supergravity. A symplectic and coordinate covariant framework is established, which allows one to discuss stringy `classical and quantum duality symmetries'…
The BPS states of N=2 super Yang-Mills theory with gauge group SU(2) are constructed as non-trivial finite-energy solutions of the worldvolume theory of a threebrane probe in F theory. The solutions preserve 1/2 of N=2 supersymmetry and…
The partition function of general N = 2 supersymmetric SU(2) Yang-Mills theories on a four-sphere localizes to a matrix integral. We show that in the decompactification limit, and in a certain regime, the integral is dominated by a saddle…
We perform a systematic analysis on supersymmetric states in N=4 supersymmetric Yang-Mills theory (SYM) on R x S^3. We find a new set of 1/16 BPS equations and determine the precise configuration of the supersymmetric states by solving all…
These are notes from introductory lectures given at the Ecole Normale in Paris and at the Strasbourg meeting dedicated to the memory of Claude Itzykson. I review in considerable detail and in a hopefully pedagogical way the work of Seiberg…