Related papers: Darboux coordinates, Yang-Yang functional, and gau…
We propose a relation between the operator of S-duality (of N=4 super Yang-Mills theory in 3+1D) and a topological theory in one dimension lower. We construct the topological theory by compactifying N=4 super Yang-Mills on a circle with an…
Seiberg-Witten geometry of mass deformed $\mathcal N=2$ superconformal ADE quiver gauge theories in four dimensions is determined. We solve the limit shape equations derived from the gauge theory and identify the space $\mathfrak M$ of…
In this article, we shall develop and formulate two novel viewpoints and properties concerning the three-point functions at weak coupling in the SU(2) sector of the N = 4 super Yang-Mills theory. One is a double spin-chain formulation of…
We establish that Hitchin's connection exist for any rigid holomorphic family of Kahler structures on any compact pre-quantizable symplectic manifold which satisfies certain simple topological constraints. Using Toeplitz operators we prove…
We prove that for $SU(2)$ and $SO(3)$ quantum gauge theory on a torus, holonomy expectation values with respect to the Yang-Mills measure $d\mu_T(\o) =N_T^{-1}e^{-S_{YM}(\o)/T}[{\cal D}\o]$ converge, as $T\downarrow 0$, to integrals with…
We prove that the moduli space of solutions to the PU(2) monopole equations is a smooth manifold of the expected dimension for simple, generic parameters such as (and including) the Riemannian metric on the given four-manifold. In a…
We build nearly topological quantum field theories in various dimensions. We give special attention to the case of 8 dimensions for which we first consider theories depending only on Yang-Mills fields. Two classes of gauge functions exist…
Two-dimensional quadratic algebras are generalizations of Lie algebras that include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical…
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…
Non-commutative differential geometry allows a scalar field to be regarded as a gauge connection, albeit on a discrete space. We explain how the underlying gauge principle corresponds to the independence of physics on the choice of vacuum…
This is the second article in the collection of reviews "Exact results on N=2 supersymmetric gauge theories", ed. J. Teschner. The space of vacua of class $\cal S$ theories on $R^3 \times S^1$ can be identified as the moduli space of…
We study exact soliton solutions of anti-self-dual Yang-Mills equations for $G =GL(2)$ in four-dimensional spaces with the Euclidean, Minkowski and Ultrahyperbolic signatures and construct special kinds of one-soliton solutions whose action…
We analyze the spectrum of dyons in N=4 supersymmetric Yang-Mills theory with gauge group SU(3) spontaneously broken down to U(1)xU(1). The Higgs fields select a natural basis of simple roots. Acting with S-duality on the W-boson states…
We propose that chiral two-dimensional Yang-Mills theory on a Riemann surface is dual to a deformed stationary subsector of the Gromov-Witten theory of that Riemann surface. Firstly, we argue that the algebraic structure that underlies the…
We investigate Yang--Mills instanton theory over four dimensional asymptotically locally flat (ALF) geometries, including gravitational instantons of this type, by exploiting the existence of a natural smooth compactification of these…
Supersymmetric Yang-Mills quantum mechanics (SYMQM) results from the dimensional reduction of the Yang-Mills field theory in $D$ space-time dimensions to a single point in the $D-1$ dimensional space. It can be also viewed as the effective…
The problem of computing quantum mechanical propagators can be recast as a computation of a Wilson line operator for parallel transport by a flat connection acting on a vector bundle of wavefunctions. In this picture the base manifold is an…
We prove a Darboux theorem for formal deformations of Hamiltonian operators of hydrodynamic type (Dubrovin-Novikov). Not all deformations are equivalent to the original operator: there is a moduli 2-stack of normal forms. The paper utilizes…
In this paper we show that a particular twist of $\mathcal{N}=4$ super Yang-Mills in three dimensions with gauge group SU(2) possesses a set of classical vacua corresponding to the space of flat connections of the {\it complexified} gauge…
The general form of N=2 supergravity coupled to an arbitrary number of vector multiplets and hypermultiplets, with a generic gauging of the scalar manifold isometries is given. This extends the results already available in the literature in…