Wild Wall Crossing and BPS Giants

Following the suggestion of hep-th/0506249 and hep-th/0612011, we represent quarter BPS dyons in N=4 supersymmetric string theories as string network configuration and explore the role of genus two surfaces in determining the spectrum of such dyons. Our analysis leads to the correct contour prescription for integrating the partition function to determine the spectrum in different domains of the moduli space separated by the walls of marginal stability.

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 primitive wall-crossing formula from an asymptotic analysis of certain Dirac-type operators on monopole moduli spaces. Along the way we give an asymptotic metric for the moduli space of singular monopoles, analogous to the Gibbons-Manton and ...

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 states, are universal, and 2(n-1) dimensional classical moduli spaces M_n emerge from zero locus of the potential energy. We emphasize that there is no natural reduction of the quantum mechanics to M_n, contrary to the conventional wisdom. Never...

We study the BPS spectrum of four dimensional N=2 SU(2) theory with massive fundamental matters using the D3-brane probe. Since the BPS states are realized by string webs subject to the BPS conditions, we determine explicitly the configurations of such webs. It is observed that there appear BPS string webs with multiple of junctions corresponding to the fact that the curves of marginal stability in massive theory are infinitely nested. In terms of the string configurations, v...

We derive a localization formula for the refined index of gauged quantum mechanics with four supercharges. Our answer takes the form of a residue integral on the complexified Cartan subalgebra of the gauge group. The formula captures the dependence of the index on Fayet-Iliopoulos parameters and the presence of a generic superpotential. The residue formula provides an efficient method for computing cohomology of quiver moduli spaces. Our result has broad applications to the c...

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs br...

We formulate supersymmetric low energy dynamics for BPS dyons in strongly-coupled N=2 Seiberg-Witten theories, and derive wall-crossing formulae thereof. For BPS states made up of a heavy core state and n probe (halo) dyons around it, we derive a reliable supersymmetric moduli dynamics with 3n bosonic coordinates and 4n fermionic superpartners. Attractive interactions are captured via a set of supersymmetric potential terms, whose detail depends only on the charges and the sp...

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 the two $SU(2)$ subgroups of the $R$-symmetry. In the cases with no vanishing Chern-Simons levels, we find a pair of Wilson loops for each pair of adjacent nodes on the quiver connected by a hypermultiplet (nodes connected by twisted hypermul...

We study the spectrum of BPS domain walls within the parameter space of N=1 U(N) gauge theories with adjoint matter and a cubic superpotential. Using a low energy description obtained by compactifying the theory on R^3 x S^1, we examine the wall spectrum by combining direct calculations at special points in the parameter space with insight drawn from the leading order potential between minimal walls, i.e those interpolating between adjacent vacua. We show that the multiplicit...

In four dimensional N=2 supergravity theories, BPS bound states near marginal stability are described by configurations of widely separated constituents with nearly parallel central charges. When the vacuum moduli can be dialed adiabatically until the central charges become anti -parallel, a paradox arises. We show that this paradox is always resolved by the existence of "bound state transformation walls" across which the nature of the bound state changes, although the index ...