Related papers: Monopoles and Four-Manifolds

We study the relationship between instanton counting in N=4 Yang-Mills theory on a generic four-dimensional toric orbifold and the semi-classical expansion of q-deformed Yang-Mills theory on the blowups of the minimal resolution of the…

We review the relation of certain integrals over the Coulomb phase of $d=4$, N=2 SO(3) supersymmetric Yang-Mills theory with Donaldson-Witten theory. We describe a new way to write an important contact term in the theory and show how the…

Let $G$ be a finite subgroup of $\mathrm{SU}(4)$ whose elements have age not larger than one. In the first part of this paper, we define $K$-theoretic stable pair invariants on the crepant resolution of the affine quotient $\mathbb{C}^4/G$,…

We study the Donaldson invariants of simply connected $4$-manifolds with $b_+=1$, and in particular the change of the invariants under wall-crossing. We assume the conjecture of Kotschick and Morgan about the shape of the wall-crossing…

Using quantum field-theoretic arguments, Witten has established a relation between the Donaldson and Seiberg-Witten invariants of smooth four-manifolds. In this survey article, we describe the program to prove this relation using a moduli…

We formulate maximally supersymmetric Yang-Mills theory in five dimensions in light-cone superspace. The light-cone Hamiltonian is of the quadratic form and the theory can be understood as an oxidation of the N=4 Super Yang-Mills Theory in…

An elementary introduction into the Seiberg-Witten theory is given. Many efforts are made to get it as pedagogical as possible, within a reasonable size. The selection of the relevant material is heavily oriented towards graduate students.…

The use of supersymmetric localisation has recently led to modular covariant expressions for certain integrated correlators of half-BPS operators in $\mathcal{N} = 4$ supersymmetric Yang-Mills theory with a general classical gauge group…

Four-point functions of gauge-invariant operators in D=4, N=4 supersymmetric Yang-Mills theory are studied using N=2 harmonic superspace perturbation theory. The results are expressed in terms of differential operators acting on a scalar…

This is the third in our series of papers relating gauge theoretic invariants of certain 4-manifolds with invariants of 3-manifolds derived from Rohlin's theorem. Such relations are well-known in dimension three, starting with Casson's…

In this paper we study the holomorphic Euler characteristics of determinant line bundles on moduli spaces of rank 2 semistable sheaves on an algebraic surface X, which can be viewed as $K$-theoretic versions of the Donaldson invariants. In…

The wall-crossing formula for Donaldson invariants of smooth, simply connected four manifolds with $b^+=1$ is shown to be a topological invariant of the manifold for reducible connections with two or fewer singular points. The explicit…

Extending recent work of Kachru and Silverstein, we consider ``orbifolds'' of 4-dimensional $\mathcal{N}=4$ SU(n) super-Yang-Mills theories with respect to discrete subgroups of the SU(4) $R$-symmetry which act nontrivially on the gauge…

The connection between Yang--Mills gauge fields on $4$-dimensional orientable compact Riemannian manifolds and modified L\'evy Laplacians is studied. A modified L\'evy Laplacian is obtained from the L\'evy Laplacian by the action of an…

Recently Andrei Teleman considered instanton moduli spaces over negative definite four-manifolds $X$ with $b_2(X) \geq 1$. If $b_2(X)$ is divisible by four and $b_1(X) =1$ a gauge-theoretic invariant can be defined; it is a count of flat…

We give a one-dimensional interpretation of the four-dimensional twisted N=1 superYang-Mills theory on a Kaehler manifold by performing an appropriate dimensional reduction. We prove the existence of a 6-generator superalgebra, which does…

We study vortex-type solutions in a (4+1)-dimensional Einstein-Yang-Mills-SU(2) model. Assuming all fields to be independent on the extra coordinate, these solutions correspond in a four dimensional picture to axially symmetric…

Anti-self-dual (ASD) solutions to the Yang-Mills equation (or instantons) over an anti-self-dual four manifold, which are invariant under an appropriate action of a three dimensional Lie group, give rise, via twistor construction, to…

We study the global symmetries of the $\mathbb{Z}_2$-orbifold of N=4 Super-Yang-Mills theory and its marginal deformations. The process of orbifolding to obtain an N=2 theory would appear to break the $\mathrm{SU}(4)$ R-symmetry down to…

The equivalence of the anti-selfduality Yang-Mills equations on the 4-dimensional orientable Riemannian manifold and Laplace equations for some infinite dimensional Laplacians is proved. A class of modificated Levy Laplacians parameterized…