Decoupling and reduction in Chern–Simons modified gravity

We show that for four-dimensional spacetimes with a non-null hypersurface orthogonal Killing vector and for a Chern–Simons (CS) background (non-dynamical) scalar field, which is constant along the Killing vector, the source-free equations of CS modified gravity decouple into their Einstein and Cotton constituents. Thus, the model supports only general relativity solutions. We also show that, when the cosmological constant vanishes and the gradient of the CS scalar field is parallel to the non-null hypersurface orthogonal Killing vector of constant length, CS modified gravity reduces to topologically massive gravity in three dimensions. Meanwhile, with the cosmological constant such a reduction requires an appropriate source term for CS modified gravity.     

Analysis of Velázquez’s solution to the mean curvature flow with a type II singularity

Velázquez in 1994 used the degree theory to show that there is a perturbation of Simons’ cone, starting from which the mean curvature flow develops a type II singularity at the origin. He also showed that under a proper time-dependent rescaling of the solution around the origin, the rescaled flow converges in the C⁰ sense to a minimal hypersurface which is tangent to Simons’ cone at infinity. In this paper, we prove that the rescaled flow actually converges locally smoothly to the minimal hypersurface, which appears to be the singularity model of the type II singularity. In addition, we show that the mean curvature of the solution blows up near the origin at a rate which is smaller than that of the second fundamental form.     

Multiple Existence Results for the Self-Dual Chern–Simons–Higgs Vortex Equation

We study the asymptotic behavior for the condensate solutions of the self-dual Chern–Simons–Higgs equation as the Chern–Simons parameter tends to zero. By using these estimates, we establish existence results for solutions of non-topological type.     

Vacuum Polarisation Effects in the Lorentz Violating Electrodynamics

In this work we reconsider the one loop calculation for the vacuum polarisation tensor in the Lorentz violating quantum electrodynamics. The electron propagator is “dressed” by a Lorentz breaking extra term in the fermion Lagrangian density. We check gauge invariance and use the Schwinger–Dyson equation to discuss the full photon propagator. After a discussion on a possible photon mass shift, we show how a finite quantum correction can be chosen in a unique way in order to ensure—in the spirit of spontaneously broken theories—the standard normalisation conditions for the vacuum polarisation tensor. Then we comment on possible observable physical consequences on the Lamb-shift.     

Standing waves for the Chern–Simons–Schrödinger systems without (AR) condition

In this paper we study the nonlinear Chern–Simons–Schrödinger systems with an external potential. We show the existence, non-existence, and multiplicity of standing waves to this problem with asymptotically linear nonlinearities, which do not hold the Ambrosetti–Rabinowitz condition.     

Holographic correspondence in topological superconductors

We analytically derive a compatible family of effective field theories that uniquely describe topological superconductors in 3D, their 2D boundary and their 1D defect lines. We start by deriving the topological field theory of a 3D topological superconductor in class DIII, which is consistent with its symmetries. Then we identify the effective theory of a 2D topological superconductor in class D living on the gapped boundary of the 3D system. By employing the holographic correspondence we derive the effective chiral conformal field theory that describes the gapless modes living on the defect lines or effective boundary of the class D topological superconductor. We demonstrate that the chiral central charge is given in terms of the 3D winding number of the bulk which by its turn is equal to the Chern number of its gapped boundary.     

Chern–Simons Action on a Finite Point Space

We apply Connes' noncommutative geometry to a finite point space. The explicit Chern–Simons action on this finite point space is obtained.     

Topological Solutions in the Self-dual Chern–Simons–Higgs Theory in a Background Metric

In this Letter we show the existence of topological multi-vortex solutions in the self-dual Chern–Simons–Higgs theory in a background metric which interpolates flat spacetime and cylinder smoothly.