Related papers: Sequencing BPS Spectra
BPS spectra give important insights into the non-perturbative regimes of supersymmetric theories. Often from the study of BPS states one can infer properties of the geometrical or algebraic structures underlying such theories. In this paper…
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossing phenomena, algebras of closed…
In this note, a novel BCS-type formalism is constructed in the framework of a schematic QCD inspired quark model, having in mind the description of color symmetrical superconducting states. The physical properties of the BCS vacuum (average…
We consider the spectrum of BPS saturated states in $N = 2$ gauge theories in four dimensions. This spectrum may be discontinuous across real codimension one submanifolds of marginal stability in the moduli space of vacua. An example, which…
These notes are based on work done in collaboration with Frank Ferrari. We show how to determine the spectra of stable BPS states in $N=2$ supersymmetric $SU(2)$ Yang-Mills theories that are asymptotically free, i.e. without and with…
Contributing to the rigorous understanding of BP, in this paper we relate the convergence of BP to spectral properties of the graph. This encompasses a result for random graphs with a ``planted'' solution; thus, we obtain the first rigorous…
We discuss the restructuring of the BPS spectrum which occurs on certain submanifolds of the moduli/parameter space -- the curves of the marginal stability (CMS) -- using quasiclassical methods. We argue that in general a `composite' BPS…
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…
We study the relation between the persistent homology and the spectral sequence of a filtered chain complex over a field. Our method is based on a decomposition of the persistent homology. We demonstrate that, under fairly general…
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…
We define reduced colored sl(N) link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of…
It is possible to understand whether a given BPS spectrum is generated by a relevant deformation of a 4D N=2 SCFT or of an asymptotically free theory from the periodicity properties of the corresponding quantum monodromy. With the aim of…
In this paper we study the behavior of Hamilton operators and their spectra which depend on infinitely many coupling parameters or, more generally, parameters taking values in some Banach space. One of the physical models which motivate…
We consider the long range forces between two BPS particles on the Coulomb branch of N=2 and N=4 supersymmetric gauge theories. The 1/r potential is unambiguously fixed, even at strong coupling, by the moduli dependence of central charges…
A large class of N=2 quantum field theories admits a BPS quiver description and the study of their BPS spectra is then reduced to a representation theory problem. In such theories the coupling to a line defect can be modelled by framed…
We motivate and survey the theory of BPS invariants of categories and BPS cohomology of stacks, indicating applications in enumerative geometry and representation theory, as well as recent advances.
Effects of the band structure on the symmetry of superconducting (SC) states are studied. For a square lattice system with a nearest-neighbor attractive interaction, SC states with various symmetries are found by changing the band…
We explore the influence of an arbitrary external potential perturbation V on the spectral properties of a weakly disordered conductor. In the framework of a statistical field theory of a nonlinear sigma-model type we find, depending on the…
The BPS spectrum of certain N=2 supersymmetric field theories can be determined algebraically by studying the representation theory of BPS quivers. We introduce methods based on BPS quivers to study line defects. The presence of a line…
We discuss spectral properties of a charged quantum particle confined to a chain graph consisting of an infinite array of rings under influence of a magnetic field assuming a $\delta$-coupling at the points where the rings touch. We start…