Related papers: Seiberg-Witten theory and duality in integrable sy…
Recent developments in Seiberg-Witten theory and relations with Complex Geometry.
We present nontrivial examples of d=3 gauge theories with sixteen and eight supercharges which are infrared dual at special points in the moduli space. This duality is distinct from mirror symmetry. To demonstrate duality we construct the…
We investigate Seiberg-Witten theory in the presence of real structures. Certain conditions are obtained so that integer valued real Seiberg-Witten invariants can be defined. In general we study properties of the real Seiberg-Witten…
Toric Duality arises as an ambiguity in computing the quiver gauge theory living on a D3-brane which probes a toric singularity. It is reviewed how, in simple cases Toric Duality is Seiberg Duality. The set of all Seiberg Dualities on a…
A slice of AdS_5 is used to provide a 5D gravitational description of 4D strongly-coupled Seiberg dual gauge theories. An (electric) SU(N) gauge theory in the conformal window at large N is described by the 5D bulk, while its weakly coupled…
Geometric Langlands duality is usually formulated as a statement about Riemann surfaces, but it can be naturally understood as a consequence of electric-magnetic duality of four-dimensional gauge theory. This duality in turn is naturally…
It is known that electric-magnetic duality transformations are symmetries of the generalized Witten-Dijkgraaf-Verlinde-Verlinde (WDVV) equations. In Seiberg-Witten theory the solutions to these equations come in certain sets according to…
We discuss supersymmetric Yang-Mills theories with the multiple scales in the brane language. The issue concerns N=2 SUSY gauge theories with massive fundamental matter including the UV finite case of $n_{f}=2n_c$, theories involving…
These are expanded notes of lectures given at the summer school "Gif 2000" in Paris. They constitute the first part of an "Introduction to supersymmetry and supergravity" with the second part on supergravity by J.-P. Derendinger to appear…
It is shown that the relativistic invariance plays a key role in the study of integrable systems. Using the relativistically invariant sine-Gordon equation, the Tzitzeica equation, the Toda fields and the second heavenly equation as dual…
Superstring theories at low energy limit are described by the corresponding supergravities, and their non-perturbative D-brane/O-plane excitations are described by DBI and WZ actions. Higher derivative corrections to these effective actions…
We study a two-dimensional $\mathcal{N}=(0,2)$ supersymmetric duality and construct novel Bailey pairs for the associated elliptic genera. This framework provides a systematic method to establish the equivalence of the elliptic genera of…
We develop the dual description of $2+1$ SU(2) lattice gauge theory as interacting `abelian like' electric loops by using Schwinger bosons. "Point splitting" of the lattice enables us to construct explicit Hilbert space for the gauge…
We analyse the Seiberg Witten curve describing the N=2 gauge theory dual to the supergravity solution with fractional branes. Emphasis is given to those aspects that are related to stringy mechanism known as the enhancon. We also compare…
We review the notion of symplectic duality earlier introduced in the context of topological recursion. We show that the transformation of symplectic duality can be expressed as a composition of $x-y$ dualities in a broader context of log…
In this note, we give a method to derive the Seiberg duality by the matrix model. The key fact we used is that the effective actions given by matrix model method should be identical for both electric and magnetic theories. We demonstrate…
We study the gauge/gravity duality for theories with four dimensional ${\cal N}=2$ supersymmetries. We consider the large class of generalized quiver field theories constructed recently by one of us (D.G.). These field theories can also be…
We discuss a number of exact results in N=1 supersymmetric field theories. We review the results obtained by Seiberg in Super-Yang-Mills (SYM) theories with matter in fundamental representation. We then consider Kutasov-type SYM theories,…
The structure of S-duality in U(1) gauge theory on a 4-manifold M is examined using the formalism of noncommutative geometry. A noncommutative space is constructed from the algebra of Wilson-'t Hooft line operators which encodes both the…
We generalize previous results on N=1, (3+1)-dimensional superconformal block quiver gauge theories. It is known that the necessary conditions for a theory to be superconformal, i.e. that the beta and gamma functions vanish in addition to…