Related papers: Wall-Crossing from Boltzmann Black Hole Halos
An important question in the study of N=2 supersymmetric string or field theories is to compute the jump of the BPS spectrum across walls of marginal stability in the space of parameters or vacua. I survey four apparently different answers…
The BPS state spectrum in four-dimensional gauge theories or string vacua with N=2 supersymmetries is well known to depend on the values of the parameters or moduli at spatial infinity. The BPS index is locally constant, but discontinuous…
When formulated in twistor space, the D-instanton corrected hypermultiplet moduli space in N=2 string vacua and the Coulomb branch of rigid N=2 gauge theories on $R^3 \times S^1$ are strikingly similar and, to a large extent, dictated by…
We consider BPS states in a large class of d=4, N=2 field theories, obtained by reducing six-dimensional (2,0) superconformal field theories on Riemann surfaces, with defect operators inserted at points of the Riemann surface. Further…
The supersymmetric index in string theory can sometimes have a discontinuous integer-valued jump at co-dimension one surfaces in moduli space called walls of marginal stability. When the index counts black hole microstates, crossing such…
We derive supersymmetric quantum mechanics of n BPS objects with 3n position degrees of freedom and 4n fermionic partners with SO(4) R-symmetry. The potential terms, essential and sufficient for the index problem for non-threshold BPS…
In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay across walls of marginal stability in the space of Coulomb branch parameters, leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a…
We study $\mathcal{N}=2$ supersymmetric Yang--Mills theory in four dimensions and then compactify it on $\mathbb{R}^{3}\times S^{1}$. The gauge symmetry of the theory is broken by a vacuum expectation value of the scalar field, which…
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…
In previous work we have shown that the equivariant index of multi-centered N=2 black holes localizes on collinear configurations along a fixed axis. Here we provide a general algorithm for enumerating such collinear configurations and…
We give an elementary physical derivation of the Kontsevich-Soibelman wall crossing formula, valid for any theory with a 4d N=2 supergravity description. Our argument leads to a slight generalization of the formula, which relates monodromy…
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…
We study the quantum dynamics of a probe scalar field in the background of a black hole in AAdS spacetime in the Hamiltonian formulation of general relativity in the maximal slicing gauge. The black hole solution in this gauge is expressed…
In recent series of works, by translating properties of multi-centered supersymmetric black holes into the language of quiver representations, we proposed a formula that expresses the Hodge numbers of the moduli space of semi-stable…
We introduce a new wall-crossing formula which combines and generalizes the Cecotti-Vafa and Kontsevich-Soibelman formulas for supersymmetric 2d and 4d systems respectively. This 2d-4d wall-crossing formula governs the wall-crossing of BPS…
We study the BPS spectrum of four-dimensional $\mathcal{N}=2$ supersymmetric Yang-Mills theory with gauge group $SU(2)$ and a massive adjoint hypermultiplet, which has an extremely intricate structure with infinite spectrum in all chambers…
We study the Donaldson invariants of rational surfaces and their dependence on the chambers in the ample cone. We build on a previous joint paper in which we have expressed the change of the Donaldson invariants on an algebraic surface $S$…
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…
We outline a comprehensive and first-principle solution to the wall-crossing problem in D=4 N=2 Seiberg-Witten theories. We start with a brief review of the multi-centered nature of the typical BPS states and recall how the wall-crossing…
We study the interplay between wall-crossing in four-dimensional gauge theory and instanton contributions to the moduli space metric of the same theory on $\mathbb{R}^{3}\times S^{1}$. We consider $\mathcal{N}=2$ SUSY Yang--Mills with gauge…