Related papers: Seiberg-Witten Toda Chains and N=1 SQCD
We point out two extensions of the relation between matrix models, topological strings and N=1 supersymmetric gauge theories. First, we note that by considering double scaling limits of unitary matrix models one can obtain large N duals of…
We consider supergravity solutions of D5 branes wrapped on supersymmetric 2-cycles and use them to discuss relevant features of four-dimensional N=1 and N=2 super Yang-Mills theories with gauge group SU(n). In particular in the N=1 case,…
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 deformations of dualities in finite N=2 supersymmetric QCD. Adding mass terms for some quarks and the adjoint matter to the finite N=2 theory, which is known to have dual descriptions, the correspondence of gauge invariant…
We discuss the Seiberg-Witten solution of the non-commutative N=2 U(N) SYM model. The solution is described in terms of the ordinary Seiberg-Witten curve of the SU(N) theory plus an additional free U(1). Hence, at the two-derivative…
We study the connection problem for a class of linear differential equations of order $N$ closely related to the Baxter equation of the quantum Toda chain. The space of solutions is $N$-dimensional and several linearly independent solutions…
These lectures are devoted to the low energy limit of \N2 SUSY gauge theories, which is described in terms of integrable systems. A special emphasis is on a duality that naturally acts on these integrable systems. The duality turns out to…
We present a large set of new self-dual N=1 SUSY gauge theories. Examples include SU(N) theories with tensors and SO(N) theories with spinors. Using these dualities as starting points, new non-trivial duals can be derived by higgsing the…
In this talk I review and generalize an idea of Seiberg that an N=1 supersymmetric gauge theory shows confinement without breaking of chiral symmetry when the gauge symmetry of its magnetic dual is completely broken by the Higgs effect. It…
We investigate nonperturbative effects in N=1 and N=2 supersymmetric theories using a relation between perturbative and exact anomalies as a starting point. For N=2 supersymmetric SU(n) Yang-Mills theory we derive the general structure of…
We briefly review the place of the Toda closed chain and the Toda field theory in solution to the $\cal{N}$=2 supersymmetric Yang-Mills theory. The classical and quantum aspects of the correspondence are mentioned and the role of branes as…
We summarize recent results on the resolution of two intimately related problems, one physical, the other mathematical. The first deals with the resolution of the non-perturbative low energy dynamics of certain N=2 supersymmetric Yang-Mills…
Gravitational corrections in N=1 and N=2 supersymmetric gauge theories are obtained from topological string amplitudes. We show how they are recovered in matrix model computations. This provides a test of the proposal by Dijkgraaf and Vafa…
The Seiberg-Witten solution plays a central role in the study of N=2 supersymmetric gauge theories. As such, it provides a proving ground for a wide variety of techniques to treat such problems. In this review we concentrate on the role of…
We study Baxter's T-Q equation of XXX spin-chain models under the semiclassical limit where an intriguing SU(N)/SU(2)^{N-3} correspondence emerges. That is, two kinds of 4D \mathcal{N}=2 superconformal field theories having the above…
We present more examples of dual N=1 SUSY gauge theories. This set of theories is connected by flows to both Seiberg's and Kutasov's dual theories. This provides a unifying picture of the various dual theories. We investigate the dual…
The s-confining theories are a class of supersymmetric gauge theories with infrared dynamics which are well-understood. Perturbing such theories can give rise to dynamical supersymmetry breaking. We realize simple models of dynamical…
A reformulation of the superconformal Ward identities that combines all the superconformal currents and the associated parameters in one multiplet is given for theories with rigid N=1 or N=2 supersymmetry. This form of the Ward Identities…
We use the Dijkgraaf-Vafa technique to study massive vacua of 6D SU(N) SYM theories on tori with R-symmetry twists. One finds a matrix model living on the compactification torus with a genus 2 spectral curve. The Jacobian of this curve is…
We briefly review the Whitham hierarchies and their applications to integrable systems of the Seiberg-Witten type. The simplest example of the N=2 supersymmetric SU(2) pure gauge theory is considered in detail and the corresponding Whitham…