Related papers: Characteristic classes via 4-dimensional gauge the…

We give a proof of the existence of $G=SU(5)$, stable holomorphic vector bundles on elliptically fibered Calabi--Yau threefolds with fundamental group $\bbz_2$. The bundles we construct have Euler characteristic 3 and an anomaly that can be…

The usual action of Yang-Mills theory is given by the quadratic form of curvatures of a principal G bundle defined on four dimensional manifolds. The non-linear generalization which is known as the Born-Infeld action has been given. In this…

We present a series of four self-contained lectures on the following topics: (I) An introduction to 4-dimensional 1\leq N \leq 4 supersymmetric Yang-Mills theory, including particle and field contents, N=1 and N=2 superfield methods and the…

We show how to represent a class of expressions involving discrete sums over partitions as matrix models. We apply this technique to the partition functions of 2* theories, i.e. Seiberg-Witten theories with the massive hypermultiplet in the…

By using the gluing formula of the Seiberg-Witten invariant, we compute the Yamabe invariant Y(X) of 4-manifolds X obtained by performing surgeries along points, circles or tori on compact Kaehler surfaces. For instance, if M is a compact…

We prove the existence of many non-trivial characteristic classes of smooth oriented bundles with fibre a product $ S^{n}\times S^{n} $ of odd-dimensional spheres. We do so by proving injectivity of the map from the ring of rational…

A $Q$-manifold $M$ is a supermanifold endowed with an odd vector field $Q$ squaring to zero. The Lie derivative $L_Q$ along $Q$ makes the algebra of smooth tensor fields on $M$ into a differential algebra. In this paper, we define and study…

We study topological gauge theories with N=(2,0) supersymmetry based on stable bundles on general Kahler 3-folds. In order to have a theory that is well defined and well behaved, we consider a model based on an extension of the usual…

A relative Picard theory in the context of graded manifolds is introduced. A Berezinian calculus and a theory of connections over SUSY-curves are systematically developed, and used to prove a Gauss-Bonnet theorem for line bundles in that…

We present families of algebraic curves describing the moduli-space of $N\!=\!2$ supersymmetric Yang-Mills theory with gauge group $SO(2n)$. We test our curves by computing the weak coupling monodromies and the number of $N\!=\!1$ vacua.

It is presented the general method that allows to formulate 4D $SU(N)$ Yang - Mills theory in terms of only local gauge invariant variables. For the case N=2, that is discussed in details, this gauge invariant formulation appears to be very…

The construction of twisted K-theory classes on a compact Lie group is reviewed using the supersymmetric Wess-Zumino-Witten model on a cylinder. The Quillen superconnection is introduced for a family of supercharges parametrized by a…

We derive four dimensional gauge theories with exceptional groups $F_4$, $E_8$, $E_7$, and $E_7$ with matter, by starting from the duality between the heterotic string on $K3$ and F-theory on a elliptically fibered Calabi-Yau 3-fold. This…

Bundle gerbes are a higher version of line bundles, we present nonabelian bundle gerbes as a higher version of principal bundles. Connection, curving, curvature and gauge transformations are studied both in a global coordinate independent…

We introduce an invariant of tuples of commutative diffeomorphisms on a 4-manifold using families of Seiberg-Witten equations. This is a generalization of Ruberman's invariant of diffeomorphisms defined using 1-parameter families of…

Using characters of finite group representations and monodromy of matter curves in F-GUT, we complete partial results in literature by building SO$% _{10}$ models with dihedral $\mathbb{D}_{4}$ discrete symmetry. We first revisit the…

By extending a result of Kronheimer-Mrowka to the family setting, we prove a gluing formula for the family Seiberg-Witten invariant. This formula allows one to compute the invariant for a smooth family of 4-manifolds by cutting it open…

We construct the Seiberg-Witten theory on 3-manifolds with Euclidean ends (connected sums of $\R^3$ and a compact manifold) with perturbations which approximate $*dx_3$ at infinity, and describe the structure of the moduli spaces. The setup…

Symplectic 4-manifolds $(X,\omega)$ with $b_+{=}1$ are roughly classified by the canonical class $K$ and the symplectic form $\omega$ depending upon the sign of $K^2$ and $K\cdot \omega$. Examples are known for each category except for the…

To explore color/kinematics duality for general representations of the gauge group we formulate the duality for general abelian orbifolds of the SU(N), N=4 super Yang-Mills theory in four dimensions, which have fields in the bi-fundamental…