Related papers: Wall Crossing Structures and Application to SU(3) …
We survey recent developments on Donaldson-Thomas theory, Bridgeland stability conditions and wall-crossing formula. We emphasize the importance of the counting theory of Bridgeland semistable objects in the derived category of coherent…
We determine the wall divisors on irreducible symplectic orbifolds which are deformation equivalent to a special type of examples, called Nikulin orbifolds. The Nikulin orbifolds are obtained as partial resolutions in codimension 2 of a…
We explore Seiberg-like dualities, or mutations, for ${\cal N}=4$ quiver quantum mechanics in the context of wall-crossing. In contrast to higher dimensions, the 1d Seiberg-duality must be performed with much care. With fixed…
We explore the physics of two-body decay of BPS states using semiclassical analysis to construct explicit solutions that illustrate the main features of wall crossing, for both ordinary and framed BPS states. In particular we recover the…
For a Calabi-Yau 3-fold $X$, we explicitly compute the Donaldson-Thomas type invariant counting pairs $(F, V)$, where $F$ is a zero-dimensional coherent sheaf on $X$ and $V\subset F$ is a two dimensional linear subspace, which satisfy a…
An old conjecture claims that commuting Hamiltonians of the double-elliptic integrable system are constructed from the theta-functions associated with Riemann surfaces from the Seiberg-Witten family, with moduli treated as dynamical…
This is the second paper in a series on intrinsic Donaldson-Thomas theory, a framework for studying the enumerative geometry of general algebraic stacks. In this paper, we present the construction of Donaldson-Thomas invariants for general…
We study the BPS spectrum and walls of marginal stability of the $\mathcal{N}=2$ supersymmetric theory in four dimensions with gauge group SU(n) and $n\le N_{f}<2n$ fundamental flavours at the root of the Higgs branch. The strong-coupling…
This is the third installment in our series of articles (dg-ga/9712005, dg-ga/9710032) on the application of the PU(2) monopole equations to prove Witten's conjecture (hep-th/9411102) concerning the relation between the Donaldson and…
Recently an exact duality between topological string and the spectral theory of operators constructed from mirror curves to toric Calabi-Yau threefolds has been proposed. At the same time an exact quantization condition for the cluster…
There are two families of Donaldson invariants for the complex projective plane, corresponding to the SU(2)-gauge theory and the SO(3)-gauge theory with non-trivial Stiefel-Whitney class. In 1997 Moore and Witten conjectured that the…
We propose generating functions which encode the degeneracies and wall-crossing phenomena of $\mathcal{N}=2$ BPS structures. The generating functions have a representation-theoretic origin and are the analogs of the 1/4-BPS dyon counting…
We study the moduli space of $SU(4)$ invariant BPS conditions in supersymmetric gauge theory on non-commutative ${\mathbb C}^4$ by means of an ADHM-like quiver construction and we classify the invariant solutions under the natural toric…
The aim of this paper is to construct the cohomological Hall algebras for $3$-Calabi--Yau categories admitting a strong orientation data. This can be regarded as a mathematical definition of the algebra of BPS states, whose existence was…
In this paper, we study holomorphic discs in K3 surfaces and defined the open Gromov-Witten invariants. Using this new invariant, we can establish a version of correspondence between tropical discs and holomorphic discs with non-trivial…
We study the classification of symmetry protected topological (SPT) phases with crystalline symmetry (cSPT phases). Focusing on bosonic cSPT phases in two and three dimensions, we introduce a simple family of cSPT states, where the system…
We study a realization of S dualities of four-dimensional $\mathcal{N}=2$ class $\mathcal{S}$ theories based on BPS graphs. S duality transformations of the UV curve are explicitly expressed as a sequence of topological transitions of the…
A simple mechanism for SUSY breaking is proposed due to the coexistence of BPS domain walls. It requires no messenger fields nor complicated SUSY breaking sector on any of the walls. We assumed that our world is on a BPS domain wall and…
We argue that certain BPS states in the D3-brane probe realization of N=2 SU(2) Super-Yang-Mills theory correspond to multi-pronged strings connecting the D3-brane to the background 7-branes. This provides a physical realization of the…
We formulate a very general conjecture relating the analytical invariants of a normal surface singularity to the Seiberg-Witten invariants of its link provided that the link is a rational homology sphere. As supporting evidence, we…