Boundary conditions and renormalized stress-energy tensor on a Poincar\'e patch of $\textrm{AdS}_2$
| Autor: | João Paulo M. Pitelli, Ricardo A. Mosna, Vitor S. Barroso |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Physics
High Energy Physics - Theory 010308 nuclear & particles physics Boundary (topology) Space (mathematics) 01 natural sciences Dirichlet distribution General Relativity and Quantum Cosmology symbols.namesake 0103 physical sciences symbols Stress–energy tensor Tensor Boundary value problem Quantum field theory 010306 general physics Scalar field Mathematical physics |
| Popis: | 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 $T_{\mu\nu}$ for a scalar field $\phi$ on the Poincar\'e patch of $\text{AdS}_2$ 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 $\textrm{AdS}$ invariance. As a result, $\langle\phi^2\rangle$ acquires a space dependence and $\langle T_{\mu\nu}\rangle$ is no longer proportional to the metric. When the physical quantities are expanded in a parameter $\beta$ which characterizes the boundary conditions (with $\beta=0$ corresponding to Dirichlet and $\beta=\infty$ corresponding to Neumann), the singularity of the Green's function is entirely subtracted at zeroth order in $\beta$. 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 version |
| Databáze: | OpenAIRE |
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