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    Tolerance After Liver Transplantation: Where Are We?

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    Boundary conditions and renormalized stress-energy tensor on a Poincar\'e patch of AdS2\textrm{AdS}_2

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    Quantum field theory on anti-de Sitter spacetime requires the introduction of boundary conditions at its conformal boundary, due essentially to the absence of global hyperbolicity. Here we calculate the renormalized stress-energy tensor TμνT_{\mu\nu} for a scalar field ϕ\phi on the Poincar\'e patch of AdS2\text{AdS}_2 and study how it depends on those boundary conditions. We show that, except for the Dirichlet and Neumann cases, the boundary conditions break the maximal AdS\textrm{AdS} invariance. As a result, ϕ2\langle\phi^2\rangle acquires a space dependence and Tμν\langle T_{\mu\nu}\rangle is no longer proportional to the metric. When the physical quantities are expanded in a parameter β\beta which characterizes the boundary conditions (with β=0\beta=0 corresponding to Dirichlet and β=\beta=\infty corresponding to Neumann), the singularity of the Green's function is entirely subtracted at zeroth order in β\beta. As a result, the contribution of nontrivial boundary conditions to the stress-energy tensor is free of singular terms.Comment: 7 pages. Minor Correction. Matches published versio