Vacuum densities for a brane intersecting the AdS boundary

TL;DR

This paper analyzes vacuum densities and energy-momentum tensor expectations for a scalar field in AdS spacetime with a brane, revealing decay behaviors and boundary condition effects on vacuum energy distribution.

Contribution

It provides a detailed study of vacuum expectation values in AdS with a brane under Robin boundary conditions, highlighting decay behaviors and boundary condition influences.

Findings

Brane-induced vacuum expectation values decay as power-law at large distances.

Boundary conditions significantly affect the sign of energy density near the brane.

Neumann boundary condition acts as an attractor near the AdS boundary, Dirichlet near the horizon.

Abstract

We investigate the Wightman function, the mean field squared and the vacuum expectation values of energy-momentum tensor for a scalar field in AdS spacetime, in the presence of a brane perpendicular to the AdS boundary. On the brane the field operator obeys Robin boundary condition. The vacuum expectation values are decomposed into the boundary-free AdS and brane-induced contributions. In this way, for points away from the brane, the renormalization is reduced to the one in pure AdS spacetime. It is shown that at proper distances from the brane larger than the AdS curvature radius the brane-induced expectation values decay as power-law for both massless and massive scalars. This behavior is in contrast to that for a plane boundary in Minkowski spacetime, with an exponential decay for massive fields. For Robin boundary conditions different from Dirichlet and Neumann ones, the brane-induced part in the energy density is positive near the brane and negative at large distances. For Dirichlet/Neumann boundary condition the corresponding energy density is negative/positive everywhere. We show that, for a fixed value of the proper distance from the brane, near the AdS boundary, the Neumann boundary condition is an "attractor" in the general class of Robin boundary conditions, whereas Dirichlet boundary condition is an "attractor" near the horizon.