Related papers: Wall-crossing, Toric divisor and Seiberg duality
We consider the Witten index ${\cal I}= Tr (-1)^F$ of SU(2) Super-Yang-Mills quantum mechanics (SYMQ) with N=16, 8, 4 supersymmetries. The theory governs the interactions between a pair of D-branes under various circumstances, and our goal…
We study pairs of 4d N=1 supersymmetric gauge theories that share the same vacuum moduli space and the same chiral field content, encoded by a common quiver, but differ in their superpotentials. These theories arise as worldvolume theories…
We study the twisted index of 3d $\mathcal{N}=2$ supersymmetric gauge theories on $S^1 \times \Sigma$ in the presence of a real FI parameter deformation. This parameter induces a 1d FI parameter for the effective supersymmetric quantum…
Supersymmetric U(Nc) gauge theory with Nf massive hypermultiplets in the fundamental representation is given by the brane configuration made of Nc fractional Dp-branes stuck at the Z_2 orbifold singularity on Nf separated D(p+4)-branes. We…
Duality between N=1 supersymmetric gauge theories(Seiberg's duality) is geometrized, in the framework of AdS/CFT correspodences. It is shown that Seiberg's duality corresponds to monodromy of wrapped D5 branes on the homology cycles of a…
We study phase structure of the moduli space of a D0-brane on the orbifold C^3/Z_2 \times Z_2 based on stability of quiver representations. It is known from an analysis using toric geometry that this model has multiple phases connected by…
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…
We study the matrix models that describe the BPS bound states of branes arising from the quiver picture of the derived category. These theories have a topological partition function that localizes to the Euler character of the anti-ghost…
BPS spectrum with finite number of states are found for higher rank four dimensional N=2 theory engineered from six dimensional A_{N-1} (2,0) theory on a Riemann surface with various kinds of defects. The wall crossing formula is…
A key question in the study of N=2 supersymmetric string or field theories is to understand the decay of BPS bound states across walls of marginal stability in the space of parameters or vacua. By representing the potentially unstable bound…
We consider the refined $\mathrm{SU}(r)$ Vafa-Witten partition function of a smooth projective surface with non-zero holomorphic 2-form. This partition function has a vertical contribution, expressible in terms of nested Hilbert schemes.…
D-branes can end on orbifold planes if the action of the orbifold group includes (-1)^{F_L}. We consider configurations of D-branes ending on such orbifolds and study the low-energy theory on their worldvolume. We apply our results to gauge…
F-theoretic constructions can alternatively be understood as consequences of certain N = 2 Seiberg-Witten theories via type IIB r D3s probing the quantum corrected orientifold backgrounds. We present four models that come out from such…
In $D=4,N=2$ theories on $R^{3,1}$, the index receives contributions not only from single-particle BPS states, counted by the BPS indices, but also from multi-particle states made of BPS constituents. In a recent work [arXiv:1406.2360], a…
Recently, using supergravity analysis, a hyperbolic reflection group was found to underlie the structure of wall-crossing, or the discontinuous moduli dependence of the supersymmetric index due to the presence of walls of marginal…
In this article we complete the proof---for a broad class of four-manifolds---of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear…
By embedding N=2 gauge theories in string theory and utilizing string dualities we map the counting of BPS states with arbitrary electric and magnetic charges to computations of an A-model topological string on an associated geometry…
The form of the Seiberg-Witten differential is derived from the M-theory approach to N=2 supersymmetric Yang-Mills theories by directly imposing the BPS condition for twobranes ending on fivebranes. The BPS condition also implies that the…
We investigate N=(2,2) supersymmetric nonlinear sigma-models in the presence of a boundary. We restrict our attention to the case where the bulk geometry is described by chiral and twisted chiral superfields corresponding to a bihermitian…
The appearance of a generalized (or Borcherds-) Kac-Moody algebra in the spectrum of BPS dyons in N=4, d=4 string theory is elucidated. From the low-energy supergravity analysis, we identify its root lattice as the lattice of the T-duality…