Wicked metrics

Abstract

There are various ways of defining the Wick rotation in a gravitational context. There are good arguments to view it as an analytic continuation of the metric, instead of the coordinates. We focus on one very general definition and argue that it is incompatible with the requirement of preserving the field equations and the symmetries at global level: in some cases the Euclidean metric cannot be defined on the original Lorentzian manifold but only on a submanifold. This phenomenon is related to the existence of horizons, as illustrated in the cases of the de Sitter and Schwarzschild metrics.

References in corpus (20)

• Emergence of a 4D World from Causal Quantum Gravity
• Reconstructing the Universe
• Non-perturbative Lorentzian Quantum Gravity, Causality and Topology Change
• The Higgs Phenomenon in Quantum Gravity
• On Euclidean spinors and Wick rotations
• Focusing on the Fixed Point of 4D Simplicial Gravity
• Further evidence that the transition of 4D dynamical triangulation is 1st order
• Damped perturbations in the no-boundary state
• Why is Spacetime Lorentzian?
• Spinors in euclidean field theory, complex structures and discrete symmetries
• Exploring Euclidean Dynamical Triangulations with a Non-trivial Measure Term
• From configuration to dynamics -- Emergence of Lorentz signature in classical field theory
• How to Wick rotate generic curved spacetime
• Quantum Field Theory on Curved Backgrounds, I. The Euclidean Functional Integral
• On the origin of the difference between time and space
• Euclidean Dynamical Triangulation revisited: is the phase transition really 1st order? (extended version)
• Action and Observer dependence in Euclidean quantum gravity
• Emergent Lorentz Signature, Fermions, and the Standard Model
• Euclidean Action and the Einstein tensor
• Wick rotations and real GIT

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• On Gauss-bonnet gravity and boundary conditions in Lorentzian path-integral quantization
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• The phase diagram of the multi-matrix model with ABAB-interaction from functional renormalization
• Constraints on discrete global symmetries in quantum gravity
• The Spectral Geometry of de Sitter Space in Asymptotic Safety
• Configuration space for quantum gravity in a locally regularized path integral
• Visions in Quantum Gravity
• Reconstructing the graviton
• $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ in the Asymptotically Safe Standard Model
• Correlated Worldline theory: Structure and Consistency
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• Lorentzian quantum cosmology in novel Gauss-Bonnet gravity from Picard-Lefschetz methods
• Towards a Higgs mass determination in asymptotically safe gravity with a dark portal
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• Quantum fields without Wick rotation