Supersymmetric solitons and a degeneracy of solutions in AdS/CFT

We study Lorentzian supersymmetric configurations in D = 4 and D = 5 gauged $$ \mathcal{N} $$ N = 2 supergravity. We show that there are smooth 1/2 BPS solutions which are asymptotically AdS4 and AdS5 with a planar boundary, a compact spacelike direction and with a Wilson line on that circle. There are solitons where the S1 shrinks smoothly to zero in the interior, with a magnetic flux through the circle determined by the Wilson line, which are AdS analogues of the Melvin fluxtube. There is also a solution with a constant gauge field, which is pure AdS. Both solutions preserve half of the supersymmetries at a special value of the Wilson line. There is a phase transition between these two saddle-points as a function of the Wilson line precisely at the supersymmetric point. Thus, the supersymmetric solutions are degenerate, at least at the supergravity level. We extend this discussion to one of the Romans solutions in four dimensions when the Euclidean boundary is S1× Σg where Σg is a Riemann surface with genus g > 0. We speculate that the supersymmetric state of the CFT on the boundary is dual to a superposition of the two degenerate geometries.

Magnetoelectric boundary simulated by a Chern–Simons-like model

In this work we study some physical phenomena that emerge in the vicinity of a magnetoelectric boundary. For simplicity, we restrict to the case of a planar boundary described by a coupling between the gauge field with a planar external Chern–Simons-like potential. The results are obtained exactly. We compute the correction undergone by the photon propagator due to the presence of the Chern–Simons coupling and we investigate the interaction between a stationary point-like charge and the magnetoelectric boundary. In the limit of a perfect mirror, where the coupling constant between the field and the potential diverges, we recover the image method. For a non perfect mirror, we show that we have an attenuated image charge and, in addition, an image magnetic monopole whose field strength does not exhibit the presence of the undesirable and artificial divergences introduced by Dirac strings. We also study the interaction between the plate and a quantum particle with spin. In this case we have a kind of charge-magnetic dipole interaction due to the magnetoelectric properties of the plate.

The O(N ) model with ϕ6 potential in ℝ2 × ℝ+

We study the large N limit of O(N ) scalar field theory with classically marginal ϕ6 interaction in three dimensions in the presence of a planar boundary. This theory has an approximate conformal invariance at large N . We find different phases of the theory corresponding to different boundary conditions for the scalar field. Computing a one loop effective potential, we examine the stability of these different phases. The potential also allows us to determine a boundary anomaly coefficient in the trace of the stress tensor. We further compute the current and stress-tensor two point functions for the Dirichlet case and decompose them into boundary and bulk conformal blocks. The boundary limit of the stress tensor two point function allows us to compute the other boundary anomaly coefficient. Both anomaly coefficients depend on the approximately marginal ϕ6 coupling.

Notes on reflection and refraction of evanescent plane waves on the boundary between gainy/lossy media

Reflection and transmission (refraction) of a homogeneous plane wave at the planar boundary of two dielectric media is a well known phenomenon commonly treated in nearly all standard textbooks. Here the analysis of reflection and refraction of evanescent plane waves on the planar boundary between various combinations of lossy, gainy and lossless media is performed. It is shown that by the appropriate choice of the profile of evanescence various effects can take place.

Topologically Protected Duality on The Boundary of Maxwell-BF Theory

The Maxwell-BF theory with a single-sided planar boundary is considered in Euclidean four-dimensional spacetime. The presence of a boundary breaks the Ward identities, which describe the gauge symmetries of the theory, and, using standard methods of quantum field theory, the most general boundary conditions and a nontrivial current algebra on the boundary are derived. The electromagnetic structure, which characterizes the boundary, is used to identify the three-dimensional degrees of freedom, which turn out to be formed by a scalar field and a vector field, related by a duality relation. The induced three-dimensional theory shows a strong–weak coupling duality, which separates different regimes described by different covariant actions. The role of the Maxwell term in the bulk action is discussed, together with the relevance of the topological nature of the bulk action for the boundary physics.

PECULIARITIES OF ELECTROMAGNETIC OSCILLATIONS GENERATED BY A CHARGED PARTICLE CROSSING THE PLANAR BOUNDARY BETWEEN A CONDUCTING MEDIUM AND A VACUUM

The peculiarities of electromagnetic oscillations generated by a charged particle moving rectilinearly and uniformly have been studied when the particle crosses a planar boundary between a conducting medium and a vacuum perpendicular to that boundary. This study is based on the relevant exact analytical solutions of Maxwell equations, and the generalized Drude–Lorentz–Sommerfeld formula has been used for the dielectric function of conducting medium in the numerical calculations. The results of our investigation indicated that a charged particle may generate large amplitude oscillations in an electric field at frequencies wherein the dispersion phenomenon is essential and the real part of the conducting material’s dielectric function is negative. The results further revealed that these oscillations are localized at the planar boundary of the conducting medium and a vacuum. The possibility of using this phenomenon to generate electromagnetic radiation at large distances from the surface of a conducting medium of finite size is also discussed.