Related papers: Index Theorem for Domain Walls
We derive an action describing edge dynamics on interfaces for gauge theories (Maxwell and Yang-Mills) using the path integral. The canonical structure of the edge theory is deduced and the thermal partition function calculated. We test the…
I review domain wall fermions in vector gauge theories. Following a brief introduction, the status of lattice calculations using domain wall fermions is presented. I focus on results from QCD, including the light quark masses and spectrum,…
We develop a word mechanism applied in knot and link diagrams for the illustration of a diagrammatic property. We also give a necessary condition for determining incompressible and pairwise incompressible surfaces, that are embedded in knot…
In this paper we extend to the abstract A-framework some existence theorems for differential inclusion problems with Dirichlet boundary conditions.
We present results from a numerical study of N=1 supersymmetric Yang-Mills theory using domain wall fermions. In this particular lattice formulation of the theory, supersymmetry is expected to emerge accidentally in the continuum and chiral…
In the paper we prove an extension theorem for matrices with entries in H^{\infty}(U) for U being a Riemann surface of a special type. One of the main components of the proof is a Grauert type theorem for "holomorphic" vector bundles…
In this paper we prove a strengthening of a theorem of Chang, Weinberger and Yu on obstructions to the existence of positive scalar curvature metrics on compact manifolds with boundary. They construct a relative index for the Dirac…
In the (non-supersymmetric) Yang-Mills theory in the large N limit there exists an infinite set of non-degenerate vacua. The distinct vacua are separated by domain walls whose tension determines the decay rate of the false vacua. I discuss…
We calculate the interaction between two magnetic domain walls during their current-induced motion. This interaction produces a separation-dependent resistance and also a differential velocity, causing domains in motion to experience an…
The large-N limit of the two-dimensional non-local U$(N)$ Yang-Mills theory on an orientable and non-orientable surface with boundaries is studied. For the case which the holonomies of the gauge group on the boundaries are near the…
We discuss without proof some recent advances in the theory of distributional boundary values, and give an example to show that the condition that a piecewise smooth domain has generic corners is necessary for the existence of boundary…
We study the melting of a domain wall in free-fermion chains, where the periodic variation of the hopping amplitudes gives rise to a band structure. It is shown that the entanglement grows logarithmically in time, and the prefactor is…
It is pointed out that, contrary to some claims in the literature, the domain walls cannot be a source of a correlated at large scales primordial magnetic field, even if the fermionic modes bound on the wall had ferromagnetic properties. In…
The supersymmetric abelian Higgs model with N scalar fields admits multiple domain wall solutions. We perform a Callias-type index calculation to determine the number of zero modes of this soliton. We confirm that the most general domain…
The Geometry of planar domain walls is studied. It is argued that the planar walls indeed have plane symmetry. In the Minkowski coordinates the walls are mapped into revolution paraboloids.
An alternative to commonly used domain wall fermions is presented. Some rigorous bounds on the condition number of the associated linear problem are derived. On the basis of these bounds and some experimentation it is argued that domain…
We investigate the presence of domain walls in models described by three real scalar fields. We search for stable defect structures which minimize the energy of the static field configurations. We work out explict orbits in field space and…
We present a general approach for studying the dynamics of domain walls in biaxial ferromagnetic stripes with functionally graded Dzyaloshinskii-Moriya interaction (DMI). By engineering the spatial profile of the DMI parameter we propose…
This is an intoduction to the theory of the essentially mesoscopic phenomena for the magnetic domain walls.
We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to…