Hadamard renormalized scalar field theory on anti–de Sitter spacetime

Kent, Carl; Winstanley, Elizabeth

doi:10.1103/physrevd.91.044044

Cited by 34 publications

(89 citation statements)

References 58 publications

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“…The kinetic theory formulation gives the macroscopic SET Tαρ as the second order moment of the distribution function f : 5) where the integration measure d 3 p/p0 is Lorentz-invariant. The SET corresponding to the distribution (7.2) can be found by first performing a series expansion of the equilibrium distribution function (7.2) in powers of ǫ [18,19,20]:…”

Section: Kinetic Theory Resultsmentioning

confidence: 99%

Thermal expectation values of fermions on anti-de Sitter space-time

Ambruş

Winstanley

2017

Class. Quantum Grav.

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Abstract. Making use of the symmetries of anti-de Sitter space-time, we derive an analytic expression for the bispinor of parallel transport, from which we construct in closed form the vacuum Feynman Green's function of the Dirac field on this background. Using the imaginary time anti-periodicity property of the thermal Feynman Green's function, we calculate the thermal expectation values of the fermion condensate and stress-energy tensor and highlight the effect of quantum corrections as compared to relativistic kinetic theory results.

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Section: Kinetic Theory Resultsmentioning

confidence: 99%

Thermal expectation values of fermions on anti-de Sitter space-time

Ambruş

Winstanley

2017

Class. Quantum Grav.

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“…Here, L(X) = −S(X) is the length of the geodesic. In pure AdS d+1 , the Van Vleck-Morette determinant is given by [38] ∆(X) = L(X) sin L(X) d .…”

Section: B Wkb Approximationmentioning

confidence: 99%

Superluminal chaos after a quantum quench

Balasubramanian

Craps

Clerck

et al. 2019

J. High Energ. Phys.

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Thermal states holographically dual to black holes in Einstein gravity display maximal Lyapunov growth as well as "butterfly effect cones". We study these effects in highly non-equilibrium states, obtained from an initial thermal state by the sudden injection of energy. We do this by computing out-of-time-order correlators (OTOCs) in BTZ-Vaidya spacetimes, which describe transitions between black holes at different temperatures. If both pairs of boundary operators appearing in the OTOC are inserted before the energy injection, we recover standard results, with butterfly effect cones displaying a light-cone structure. But when one pair of operators is inserted before and the other pair after the energy injection, the Lyapunov growth saturates the chaos bounds set by the local temperatures and the butterfly effect cones can "open up", becoming superluminal, albeit in a way that does not violate causality. In the limiting case, in which the initial state is the vacuum, Lyapunov growth only starts after the energy injection. Our computations of the OTOCs are phrased in terms of gravitationally interacting particles, where fields are treated in a geodesic approximation and the eikonal phase shift is expressed in terms of stress tensors and shock waves associated to geodesics. arXiv:1908.08955v1 [hep-th]

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“…Also the construction of a maximally symmetric two-point function was tackled before, see [19,20]. Other recent works for this and other matter fields on AdS include [21,22]. Yet, these works considered only the special case of the Dirichlet boundary condition, which corresponds to the Friedrichs extension of the Helmholtz operator built out of the PAdS d+1 metric at constant time.…”

Section: Introductionmentioning

confidence: 99%

Hadamard states for a scalar field in anti–de Sitter spacetime with arbitrary boundary conditions

Dappiaggi

Ferreira

2016

Phys. Rev. D

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We consider a real, massive scalar field on PAdS d+1 , the Poincaré domain of the (d + 1)-dimensional anti-de Sitter (AdS) spacetime. We first determine all admissible boundary conditions that can be applied on the conformal boundary, noting that there exist instances where "bound states" solutions are present. Then, we address the problem of constructing the two-point function for the ground state satisfying those boundary conditions, finding ultimately an explicit closed form. In addition, we investigate the singularities of the resulting two-point functions, showing that they are consistent with the requirement of being of Hadamard form in every globally hyperbolic subregion of PAdS d+1 and proposing a new definition of Hadamard states which applies to PAdS

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Hadamard renormalized scalar field theory on anti–de Sitter spacetime

Cited by 34 publications

References 58 publications

Thermal expectation values of fermions on anti-de Sitter space-time

Thermal expectation values of fermions on anti-de Sitter space-time

Superluminal chaos after a quantum quench

Hadamard states for a scalar field in anti–de Sitter spacetime with arbitrary boundary conditions

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