Hadamard renormalized scalar field theory on anti-de Sitter space-time

Abstract

We consider a real massive free quantum scalar field with arbitrary curvature coupling on $n$-dimensional anti-de Sitter space-time. We use Hadamard renormalization to find the vacuum expectation values of the quadratic field fluctuations and the stress-energy tensor, presenting explicit results for $n=2$ to $n=11$ inclusive.

arXiv commentVersion accepted for publication in Physical Review D, 26 pages, 5 figures

References in corpus (22)

• Gauge Theory Correlators from Non-Critical String Theory
• Large N Field Theories, String Theory and Gravity
• Twenty Years of the Weyl Anomaly
• Hadamard renormalization of the stress-energy tensor for a quantized scalar field in a general spacetime of arbitrary dimension
• Scalar field quantization on the 2+1 dimensional black hole background
• Comments on the Stress-Energy Tensor Operator in Curved Spacetime
• Self-Force Calculations with Matched Expansions and Quasinormal Mode Sums
• Quantum Scalar Fields on Anti-de Sitter Spacetime
• van Vleck determinants: geodesic focussing and defocussing in Lorentzian spacetimes
• One-loop Quantum Gravity in Schwarzschild Spacetime
• On the Stress-Energy Tensor of Quantum Fields in Curved Spacetimes - Comparison of Different Regularization Schemes and Symmetry of the Hadamard/Seeley-DeWitt Coefficients
• One-loop stress-tensor renormalization in curved background: the relation between $\zeta$-function and point-splitting approaches, and an improved point-splitting procedure
• Quasi-local contribution to the scalar self-force: Geodesic Motion
• Vacuum polarization in asymptotically anti-de Sitter black hole geometries
• DeWitt-Schwinger Renormalization and Vacuum Polarization in d Dimensions
• Vacuum Polarization on the Schwarzschild Metric with a Cosmic String
• Vacuum polarization around a three-dimensional black hole
• Static Kerr Green's Function in Closed Form and an Analytic Derivation of the Self-Force for a Static Scalar Charge in Kerr Space-Time
• Quantum field theory on the Bertotti-Robinson space-time
• Vacuum polarization near asymptotically anti-de Sitter black holes in odd dimensions
• Hadamard Renormalisation of the Stress Energy Tensor on the Horizons of a Spherically Symmetric Black Hole Space-Time
• Fully renormalized stress tensor correlator in flat space

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• The holographic Hadamard condition on asymptotically Anti-de Sitter spacetimes
• Boundary Conditions and Vacuum Fluctuations in ${\mathrm{AdS}}_4$
• Analysis of scalar and fermion quantum field theory on anti-de Sitter space-time
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• Boundary conditions and renormalized stress-energy tensor on a Poincaré patch of ${\text{AdS}}_2$
• Vacuum polarization on topological black holes
• Vacuum polarization on three-dimensional anti-de Sitter space-time with Robin boundary conditions
• Semi-Classical Backreaction on Asymptotically Anti-de Sitter Black Holes
• Vacuum polarization for varying quantum scalar field parameters in Schwarzschild-anti-de Sitter spacetime
• Aspects of the BTZ black hole interacting with fields
• Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
• Vortical Effects for Free Fermions on Anti-De Sitter Space-Time