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.

我们研究了四维全局反德西特时空上无质量、共形耦合标量场的重正化应力能量张量 (RSET)。 Robin（混合）边界条件应用于标量场。我们计算 RSET 的真空和热期望值。当应用狄利克雷或诺伊曼边界条件时，真空 RSET 是时空度量的倍数。施加 Robin 边界条件打破了真空态的最大对称性，并导致 RSET 的混合指数分量在时空原点处具有最大值（或最大幅度）。该最大值取决于边界条件。我们发现热态有类似的行为。随着温度降低，RSET 的热预期值接近真空状态的热预期值，并且它们的值很大程度上取决于边界条件。随着温度升高，RSET 分量的值趋向于在所有边界条件下都相同的分布。我们还发现，对于真空和热态，时空边界上的 RSET 与边界条件无关，完全由迹异常决定。