Renormalized stress-energy tensor on global anti-de Sitter space-time with Robin boundary conditions

TL;DR

This paper analyzes the renormalized stress-energy tensor for a scalar field in anti-de Sitter space with Robin boundary conditions, revealing how boundary conditions influence the tensor's behavior in vacuum and thermal states.

Contribution

It provides the first detailed computation of the RSET under Robin boundary conditions in AdS space, showing how boundary conditions break symmetry and affect the tensor's properties.

Findings

Vacuum RSET is proportional to the metric under Dirichlet or Neumann conditions.

Robin boundary conditions break maximal symmetry and alter RSET maxima.

Thermal RSET approaches vacuum values at low temperature and becomes boundary-condition independent at high temperature.

Abstract

We study the renormalized stress-energy tensor (RSET) for a massless, conformally coupled scalar field on global anti-de Sitter space-time in four dimensions. Robin (mixed) boundary conditions are applied to the scalar field. We compute both the vacuum and thermal expectation values of the RSET. The vacuum RSET is a multiple of the space-time metric when either Dirichlet or Neumann boundary conditions are applied. Imposing Robin boundary conditions breaks the maximal symmetry of the vacuum state and results in an RSET whose components with mixed indices have their maximum (or maximum magnitude) at the space-time origin. The value of this maximum depends on the boundary conditions. We find similar behaviour for thermal states. As the temperature decreases, thermal expectation values of the RSET approach those for vacuum states and their values depend strongly on the boundary conditions. As the temperature increases, the values of the RSET components tend to profiles which are the same for all boundary conditions. We also find, for both vacuum and thermal states, that the RSET on the space-time boundary is independent of the boundary conditions and determined entirely by the trace anomaly.