Related papers: Four-dimensional wall-crossing via three-dimension…
We test a recently proposed wall-crossing formula for the change of the Hilbert space of BPS states in d=4,N=2 theories. We study decays of D4D2D0 systems into pairs of D4D2D0 systems and we show how the wall-crossing formula reproduces…
We give a self-contained proof of the Kontsevich-Soibelman wall-crossing formula entirely in the scope of quadratic differentials without relying on input from DT theory. Our approach is based on path-lifting rules for spectral networks…
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…
BPS equations and wall solutions are studied keeping (part of) supersymmetry (SUSY) manifest. Using N=1 superfields, massive hyper-Kahler quotient is introduced to obtain massive N=2 (8 SUSY) nonlinear sigma models in four dimensions with…
We consider BPS domain walls in the four dimensional N=1 supersymmetric models with continuous global symmetry. Since the BPS equation is covariant under the global transformation, the solutions of the BPS walls also have the global…
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…
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…
We define rational numbers counting holomorphic disks bounding a complex lagrangian submanifold on a hyperkhaler manifold of real dimension four. We provide a simple a direct proof of Kontsevich-Soibelman Wall Crossing Formula for these…
We calculate a wall crossing formula for 4-dimensional Poincare-Einstein metrics, through a wall made of orbifold Poincare-Einstein metrics with A1 singularities. This is based on a formalism which enables to deal with higher order terms of…
The Kontsevich-Soibelman wall-crossing formula is known to control the jumping behavior of BPS state counting indices in four-dimensional theories with $\mathcal{N}=2$ supersymmetry. The formula can take two equivalent forms: a…
We compute the Witten index of one-dimensional gauged linear sigma models with at least ${\mathcal N}=2$ supersymmetry. In the phase where the gauge group is broken to a finite group, the index is expressed as a certain residue integral. It…
A new simple mechanism for SUSY breaking is proposed due to the coexistence of BPS domain walls. It is assumed that our world is on a BPS domain wall and that the other BPS wall breaks the SUSY preserved by our wall. This mechanism requires…
Four-dimensional massive N=2 nonlinear sigma models and BPS wall solutions are studied in the off-shell harmonic superspace approach in which N=2 supersymmetry is manifest. The general nonlinear sigma model can be described by an analytic…
A BPS exact wall solution is found in N=1 supergravity in four dimensions. The model uses chiral scalar field with a periodic superpotential admitting winding numbers. Maintaining the periodicity in supergravity requires a gravitational…
We investigate BPS states in 4d N=4 supersymmetric Yang-Mills theory and the corresponding (p, q) string networks in Type IIB string theory. We propose a new interpretation of the algebra of line operators in this theory as a tensor product…
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 the wall-crossing phenomena of BPS D4-D2-D0 states on the conifold and orbifold C^2/Z_2, from the viewpoint of the quiver quantum mechanics on the D-branes. The Kahler moduli dependence of the BPS index is translated into the FI…
We prove an analytic version of the Kontsevich-Soibelman wall-crossing formula describing how the number of finite-length trajectories of a quadratic differential jumps as the differential is varied. We characterize certain birational…
We study BPS saturated domain walls in the supersymmetric SU(2) gauge theory. For a theory with a very light adjoint scalar (mass <~ Lambda/400) we use the perturbed N=2 Seiberg-Witten theory to calculate the actual field configuration of…
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…