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We classify the cosmological behaviors of the domain wall under junctions between two spacetimes in terms of various parameters: cosmological constants of bulk spacetime, a tension of a domain wall, and mass parameters of the black hole-type metric. Especially, we consider the false-true vacuum type junctions and the domain wall connecting between an inner AdS space and an outer AdS Reissner-Nordstr${rm ddot{o}}$m black hole. We find that there exist a solution to the junction equations with an inflation at earlier times and an accelerating expansion at later times.
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We discuss 1/2 BPS domain walls in the 3d $mathcal N=4$ supersymmetric gauge theory which is self-dual under the 3d mirror symmetry. We find that if a BF-type coupling is introduced, invariance of the BPS domain wall under the duality transformation can be explicitly seen from the classical BPS equations. It has been known that particles and vortices are swapped under the 3d duality transformations. We show that Noether charges and vortex topological charges localized on the domain walls are correctly exchanged under the 3d mirror symmetry.
We reformulate the mod-two Atiyah-Patodi-Singer (APS) index in a physicist-friendly way using the domain-wall fermion. Our new formulation is given on a closed manifold, which is extended from the original manifold with boundary, where we instead give a fermion mass term changing its sign at the location of the original boundary. This new setup does not need the APS boundary condition, which is non-local. A mathematical proof of equivalence between the two different formulations is given by two different evaluations of the same index of a Dirac operator on a higher dimensional manifold. The domain-wall fermion allows us to separate the edge and bulk mode contributions in a natural but not in a gauge invariant way, which offers a straightforward description of the global anomaly inflow.
We consider here the interaction of scalar bosons with a topological domain wall. Not only is there a continuum of scattering states, but there is also an interesting quasi-discretuum of positive energy bosonic bound states, describing bosons entrapped within the walls core. The full spectrum of the scattering and bound state energies and eigenstates is obtainable from a Schrodinger-type of equation with a Poschl-Teller potential. We also consider the presence of a boson gas within the wall and high energy boson emission.
We consider the change in the asymptotic behavior of solutions of the type of flat domain walls (i.e., kink solutions) in field-theoretic models with a real scalar field. We show that when the model is deformed by a bounded deforming function, the exponential asymptotics of the corresponding kink solutions remain exponential, while the power-law ones remain power-law. However, the parameters of these asymptotics, which are related to the wall thickness, can change.
Backreaction of excitations on a planar domain wall in a real scalar field model is investigated in the cases of homogeneous, plane wave and wave packet type excitations. It is found that the excited domain wall radiates. The method of calculating backreaction for the general forms of excitations is also presented.
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