Related papers: Vafa-Witten theory and iterated integrals of modul…
On a polarised surface, solutions of the Vafa-Witten equations correspond to certain polystable Higgs pairs. When stability and semistability coincide, the moduli space admits a symmetric obstruction theory and a $\mathbb C^*$ action with…
We consider four-dimensional Omega-deformed N=2 supersymmetric SU(2) gauge theory on A1 space and its lift to five dimensions. We find that the partition functions can be reproduced via special geometry and the holomorphic anomaly equation.…
We use the holomorphic anomaly equation to solve the gravitational corrections to Seiberg-Witten theory and a two-cut matrix model, which is related by the Dijkgraaf-Vafa conjecture to the topological B-model on a local Calabi-Yau manifold.…
We analyze the coefficients of partition functions of Vafa-Witten theory for the complex projective plane $\mathbb{CP}^2$. We experimentally study the growth of the coefficients for gauge group $SU(2)$ and $SU(3)$, which are examples of…
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…
Definition of the partition function of U(1) gauge theory is extended to a class of four-manifolds containing all compact spaces and certain asymptotically locally flat (ALF) ones including the multi-Taub--NUT spaces. The partition function…
We propose a modular anomaly equation for the prepotential of the N=2* super Yang-Mills theory on R^4 with gauge group U(N) in the presence of an Omega-background. We then study the behaviour of the prepotential in a large-N limit, in which…
We give dual interpretations of Seiberg-Witten and Dijkgraaf-Vafa (or matrix model) curves in n=1 supersymmetric U(N) gauge theory. This duality interchanges the rank of the gauge group with the degree of the superpotential; moreover, the…
Mass perturbations of the twisted N=4 supersymmetric gauge theory considered by Vafa and Witten to test S-duality are studied for the case of Kahler four-manifolds. It is shown that the resulting mass-perturbed theory can be regarded as an…
Classically, the dual under the Seiberg-Witten map of noncommutative U(N), {\cal N}=1 super Yang-Mills theory is a field theory with ordinary gauge symmetry whose fields carry, however, a \theta-deformed nonlinear realisation of the {\cal…
We study twisted N=2 superconformal gauge theory on a product of two Riemann surfaces Sigma and C. The twisted theory is topological along C and holomorphic along Sigma and does not depend on the gauge coupling or theta-angle. Upon…
U(1) gauge theory on ${\bf R}^4$ is known to possess an electric-magnetic duality symmetry that inverts the coupling constant and extends to an action of $SL(2,{\bf Z})$. In this paper, the duality is studied on a general four-manifold and…
Gorsky et al. presented an explicit construction of Whitham deformations of the Seiberg-Witten curve for the $SU(N+1)$ $\calN = 2$ SUSY Yang-Mills theory. We extend their result to all classical gauge groups and some other cases such as the…
We present an explicit expression for the topological invariants associated to $SU(2)$ monopoles in the fundamental representation on spin four-manifolds. The computation of these invariants is based on the analysis of their corresponding…
At a generic point in the moduli space of vacua of an N=4 supersymmetric gauge theory with arbitrary gauge group the Higgs force does not cancel the magneto-static force between magnetic monopoles of distinct charge. As a consequence the…
Using the Mathai-Quillen formalism we reexamine the twisted N=4 supersymmetric model of Vafa-Witten theory. Smooth out the relation between the supersymmetric action and the path integral representation of the Thom class.
The Vafa-Witten equations on an oriented Riemannian 4- manifold are first order, non-linear equations for a pair of connection on a principle SO(3) bundle over the 4-manifold and a self-dual 2-form with values in the associated Lie algebra…
A study of the gauged Wess-Zumino-Witten models is given focusing on the effect of topologically non-trivial configurations of gauge fields. A correlation function is expressed as an integral over a moduli space of holomorphic bundles with…
In this thesis we discuss recent new insights in the structure of the moduli space of flat connections of Yang-Mills theory on a 3-torus. Chapter 2 discusses the computation of Witten's index for 4-dimensional gauge theories, and the…
We investigate the electromagnetic duality properties of an abelian gauge theory on a compact oriented four-manifold by analysing the behaviour of a generalised partition function under modular transformations of the dimensionless coupling…