Related papers: Generating functions for $\mathcal{N}=2$ BPS struc…
We construct the BPS quivers with superpotential for the 4d N=2 gauge theories with non-simply laced Lie groups (B_n, C_n, F_4 and G_2). The construction is inspired by the BIKMSV geometric engineering of these gauge groups as non-split…
We present a survey of the computation of the BPS spectrum of a general four-dimensional N=2 supersymmetric gauge theory in terms of the Representation Theory of quivers with superpotential. We focus on SYM with a general gauge group G…
We describe a universal element in the group algebra of symmetric groups, whose characters provides the counting of quarter and eighth BPS states at weak coupling in N=4 SYM, refined according to representations of the global symmetry…
We generalize B. Kostant's construction of generating functions to the case of multiply-laced diagrams and we prove for this case W. Ebeling's theorem which connects the Poincare series [P_G(t)]_0 and the Coxeter transformations. According…
We construct 3d, N=2 supersymmetric gauge theories by considering a one-parameter `R-flow' of 4d, N=2 theories, where the central charges vary while preserving their phase order. Each BPS state in 4d leads to a BPS particle in 3d, and thus…
We give a formula for the bivariate generating function of a stationary 1-dependent counting process in terms of its run probability generating function, with a probabilistic proof. The formula reduces to the well known bivariate generating…
We consider some aspects of counting BPS operators which are annihilated by two supercharges, in superconformal field theories. For non-zero coupling, the corresponding multi-variable partition functions can be written in terms of…
We study the relation between the instanton counting on ALE spaces and the BPS state counting on a toric Calabi-Yau three-fold. We put a single D4-brane on a divisor isomorphic to A_{N-1}-ALE space in the Calabi-Yau three-fold, and evaluate…
We show that the BPS spectrum of pure SU(3) four-dimensional super Yang-Mills with N=2 supersymmetry exhibits a surprising phenomenon: there are regions of the Coulomb branch where the growth of the BPS degeneracies with the charge is…
For the hypergeometric spectral curve and its confluent degenerations (spectral curves of "hypergeometric type"), we obtain a simple formula expressing the topological recursion free energies as a sum over BPS states (degenerate spectral…
We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones that are invariant under the action of a…
We initiate the study of $1/2$ BPS Wilson loops in $\mathcal{N}=4$ Chern-Simons-matter theories in three dimensions. We consider a circular or linear quiver with Chern-Simons levels $k$, $-k$ and $0$, and focus on loops preserving one of…
We study the BPS states of a D6-brane wrapping the conifold and bound to collections of D2 and D0 branes. We find that in addition to the complexified Kahler parameter of the rigid sphere it is necessary to introduce an extra real parameter…
A closed expression is given for the generating function of (virtual) Poincar\'e polynomials of moduli spaces of semi-stable sheaves on the projective plane $\mathbb{P}^2$ with arbitrary rank $r$ and Chern classes. This generating function…
We give a physical explanation of the Kontsevich-Soibelman wall-crossing formula for the BPS spectrum in Seiberg-Witten theories. In the process we give an exact description of the BPS instanton corrections to the hyperkahler metric of the…
Recently, Banderier et. al. considered Young tableaux with walls, which are similar to standard Young tableaux, except that local decreases are allowed at some walls. We count the numbers $\overline{f}_m(n)$ of Young tableaux of shape…
The purpose of this brief note is to understand the reason for the appearance of a genus two Riemann surface in the expression for the microscopic degeneracy of 1/4 BPS dyons in N=4 String Theory.
The perturbative spectrum of BPS-states in the E_8 x E_8 heterotic string theory compactified on T^2 is analysed. We show that the space of BPS-states forms a representation of a certain Borcherds algebra G which we construct explicitly…
To every 3-manifold M one can associate a two-dimensional N=(2,2) supersymmetric field theory by compactifying five-dimensional N=2 super-Yang-Mills theory on M. This system naturally appears in the study of half-BPS surface operators in…
We study geometric engineering of Argyres-Douglas superconformal theories realized by type IIB strings propagating in singular Calabi-Yau threefolds. We use this construction to count the degeneracy of light BPS states under small…