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arXiv:hep-th/9704169 · Modern Physics Letters A

Quantum Decoherence in a D-Foam Background

John R. Ellis, Nick E. Mavromatos, D.V. Nanopoulos

Published Aug 10, 1997• 40 citations
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Abstract

Within the general framework of Liouville string theory, we construct a model for quantum D-brane fluctuations in the space–time background through which light closed-string states propagate. The model is based on monopole and vortex defects on the worldsheet, which have been discussed previously in a treatment of (1+1)-dimensional black hole fluctuations in the space–time background, and makes use of a T-duality transformation to relate formulations with Neumann and Dirichlet boundary conditions. In accordance with previous general arguments, we derive an open quantum-mechanical description of this D-brane foam which embodies momentum and energy conservation and small mean energy fluctuations. Quantum decoherence effects appear at a rate consistent with previous estimates.

DOI
10.1142/s0217732397001795

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Within the general framework of Liouville string theory, we construct a model for quantum D-brane fluctuations in the space–time background through which light closed-string states propagate. The model is based on monopole and vortex defects on the worldsheet, which have been discussed previously in a treatment of (1+1)-dimensional black hole fluctuations in the space–time background, and makes use of a T-duality transformation to relate formulations with Neumann and Dirichlet boundary conditions. In accordance with previous general arguments, we derive an open quantum-mechanical description of this D-brane foam which embodies momentum and energy conservation and small mean energy fluctuations. Quantum decoherence effects appear at a rate consistent with previous estimates.
We study in some detail the master equation, and its solution in a simplified case modelling flavor oscillations of a two-level system, stemming from the Liouville-string approach to quantum space-time foam. In this framework we discuss the appearance of diffusion terms and decoherence due to the interaction of low-energy string matter with space-time defects, such as D-particles in the specific model of ``D-particle foam,'' as well as dark-energy contributions. We pay particular attention to contrasting the decoherent role of a cosmological constant in inducing exponential quantum damping in the evolution of low-energy observables, such as the probability of flavor oscillations, with the situation where the dark-energy relaxes to zero for asymptotically large times, in which case such a damping is absent. Our findings may be of interest to (astrophysical) tests of quantum space-time foam models in the not-so-distant future.
We display a logarithmic divergence in the density matrix of a scalar field in the presence of an Einstein–Yang–Mills black hole in four dimensions. This divergence is related to a previously-found logarithmic divergence in the entropy of the scalar field, which cannot be absorbed into a renormalization of the Hawking–Bekenstein entropy of the black hole. Motivated by the fact that the cutoff in this divergence varies as the latter decays, by an analysis of black holes in two-dimensional string models and by studies of D-brane dynamics in higher dimensions, we propose that the renormalization scale variable be identified with time. In this case, the logarithmic divergence we find induces a non-commutator term [Formula: see text] in the quantum Liouville equation for the time evolution of the density matrix ρ of the scalar field, leading to quantum decoherence. The order of magnitude of [Formula: see text] is μ2/M P , where μ is the mass of the scalar particle.
The possible role of decoherence due to space-time foam is discussed within the context of two models, one based on string/brane theory. and the other based on properties of black hole horizons in general relativity. It is argued that the density matrix satisfies a dissipative master equation, primarily from the study of renormalization group flows in non-critical string theory.This interpretation of the zero mode of the Liouville field as time leads necessarily to the CPT operator being ill defined. One striking consequence is that the quantum mechanical correlations of pair states of neutral mesons produced in meson factories are changed from the usual EPR state. The magnitude of this departure from EPR correlations is characterised by a parameter ωωω. The predicted value of ωωω is very small or zero. However it is shown explicitly that the the non-vanishing of ωωω is only a feature of the model based on string/brane theory.
In this brief review I discuss ways and tests of CPT-Violation in the context of quantum gravity theories with space-time foam vacua, which entail quantum decoherence of matter propagating in such backgrounds. I cover a wide variety of sensitive probes, ranging from cosmic neutrinos to meson factories. I pay particular emphasis on associating the latter with specific, probably unique ('smoking-gun'), effects of this type of CPT Violation, related to a modification of Einstein-Podolsky-Rosen (EPR) correlations in the entangled states of the relevant neutral mesons. I also present some semi-microscopic estimates of these latter effects, in the context of a specific string-inspired model of space-time foam ('D-particle foam').
Abstract. The possible role of decoherence due to space-time foam is discussed within the context of two models, one based on string/brane theory. and the other based on properties of black hole horizons in general relativity. It is argued that the density matrix satisfies a dissipative master equation, primarily from the study of renormalization group flows in non-critical string theory.This interpretation of the zero mode of the Liouville field as time leads necessarily to the CPT operator being ill defined. One striking consequence is that the quantum mechanical correlations of pair states of neutral mesons produced in meson factories are changed from the usual EPR state. The magnitude of this departure from EPR correlations is characterised by a parameter ω. The predicted value of ω is very small or zero. However it is shown explicitly that the the non-vanishing of ω is only a feature of the model based on string/brane theory. 1.
We discuss two classes of semimicroscopic theoretical models of stochastic spacetime foam in quantum gravity and the associated effects on entangled states of neutral mesons, signalling an intrinsic breakdown of CPTCPTCPT invariance. One class of models deals with a specific model of foam, initially constructed in the context of noncritical (Liouville) string theory, but viewed here in the more general context of effective quantum-gravity models. The relevant Hamiltonian perturbation, describing the interaction of the meson with the foam medium, consists of off-diagonal stochastic metric fluctuations, connecting distinct mass eigenstates (or the appropriate generalization thereof in the case of KKK-mesons), and it is proportional to the relevant momentum transfer (along the direction of motion of the meson pair). There are two kinds of CPTCPTCPT-violating effects in this case, which can be experimentally disentangled: one (termed ``$\ensuremath{\omega}$-effect'') is associated with the failure of the indistinguishability between the neutral meson and its antiparticle, and affects certain symmetry properties of the initial state of the two-meson system; the second effect is generated by the time evolution of the system in the medium of the spacetime foam, and can result in time-dependent contributions of the $\ensuremath{\omega}$-effect type in the time profile of the two-meson state. Estimates of both effects are given, which show that, at least in certain models, such effects are not far from the sensitivity of experimental facilities available currently or in the near future. The other class of quantum-gravity models involves a medium of gravitational fluctuations which behaves like a ``thermal bath''. In this model both of the above-mentioned intrinsic CPTCPTCPT violation effects are not valid.