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Renormalized stress-energy tensor on global anti-de Sitter space-time with Robin boundary conditions. (arXiv:2308.05623v1 [hep-th])

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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.

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