Related papers: ADHM in 8d, coloured solid partitions and Donaldso…
We provide a contour integral formula for the exact partition function of ${\cal N}=2$ supersymmetric $U(N)$ gauge theories on compact toric four-manifolds by means of supersymmetric localisation. We perform the explicit evaluation of the…
The present paper is an extension of a previous paper written in collaboration with Markus Reineke dealing with quiver representations. The aim of the paper is to generalize the theory and to provide a comprehensive theory of…
Recent developments in the understanding of $N=2$ supersymmetric Yang-Mills theory in four dimensions suggest a new point of view about Donaldson theory of four manifolds: instead of defining four-manifold invariants by counting $SU(2)$…
We present the most general family of stationary point-like solutions of pure N=4, d=4 Supergravity characterized by completely independent electric and magnetic charges, mass, angular momentum and NUT charge plus the asymptotic values of…
We construct and study Donaldson-Thomas invariants counting orthogonal and symplectic objects in linear categories, which are a generalization of the usual Donaldson-Thomas invariants from the structure groups $\mathrm{GL} (n)$ to the…
All supersymmetric gauge theories based on simple groups which have an affine quantum moduli space, i.e. one generated by gauge invariants with no relations, W=0, and anomaly matching at the origin, are classified. It is shown that the only…
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…
We analyse the classical moduli spaces of supersymmetric vacua of 3d N=2 Chern-Simons quiver gauge theories. We show quite generally that the moduli space of the 3d theory always contains a baryonic branch of a parent 4d N=1 quiver gauge…
The ADHM construction establishes a one-to-one correspondence between framed torsion free sheaves on the projective plane and stable framed representations of a quiver with relations in the category of complex vector spaces. This paper…
We derive two multivariate generating functions for three-dimensional Young diagrams (also called plane partitions). The variables correspond to a colouring of the boxes according to a finite Abelian subgroup G of SO(3). We use the vertex…
In this paper we describe the structure of extremal stationary spherically symmetric black hole solutions in the STU model of D=4, N=2 supergravity in terms of four-qubit systems. Our analysis extends the results of previous investigations…
Solid partitions are the 4D generalization of the plane partitions in 3D and Young diagrams in 2D, and they can be visualized as stacking of 4D unit-size boxes in the positive corner of a 4D room. Physically, solid partitions arise…
We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general…
This review gives an introduction to cohomological Donaldson-Thomas theory: the study of a cohomology theory on moduli spaces of sheaves on Calabi-Yau threefolds, and of complexes in 3-Calabi-Yau categories, categorifying their numerical DT…
A supersymmetric quantum mechanical model is constructed for BPS states bound to surface operators in five dimensional SU(r) gauge theories using D-brane engineering. This model represents the effective action of a certain D2-brane…
This paper concerns the cohomological aspects of Donaldson-Thomas theory for Jacobi algebras and the associated cohomological Hall algebra, introduced by Kontsevich and Soibelman. We prove the Hodge-theoretic categorification of the…
We prove that Donaldson-Thomas type invariants are equal to weighted Euler characteristics of their moduli spaces. In particular, such invariants depend only on the scheme structure of the moduli space, not the symmetric obstruction theory…
We discover a modular property of supersymmetric partition functions of supersymmetric theories with R-symmetry in four dimensions. This modular property is, in a sense, the generalization of the modular invariance of the supersymmetric…
We present a statistical mechanical model whose random variables are solid partitions, i.e. Young diagrams built by stacking up four dimensional hypercubes. Equivalently, it can be viewed as the model of random tessellations of ${\bf…
The two-dimensional gauged linear sigma model has provided a physical model for the quantum cohomology of a K\"ahler manifold, $X$. A three-dimensional version of such construction has recently been shown to shed light on models of quantum…