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arXiv:0803.2553 · Journal of Physics A Mathematical and Theoretical

Vacuum boundary effects

M. Asorey, J. M. Munõz-Castañeda

Published Jul 15, 2008• 29 citations
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Abstract

The effect of boundary conditions on the vacuum structure of quantum field theories is analysed from a quantum information viewpoint. In particular, we analyse the role of boundary conditions on boundary entropy and entanglement entropy. The analysis of boundary effects on massless free field theories points out the relevance of boundary conditions as a new rich source of information about the vacuum structure. In all cases the entropy does not increase along the flow from the ultraviolet to the infrared.

DOI
10.1088/1751-8113/41/30/304004

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The effect of boundary conditions on the vacuum structure of quantum field theories is analysed from a quantum information viewpoint. In particular, we analyse the role of boundary conditions on boundary entropy and entanglement entropy. The analysis of boundary effects on massless free field theories points out the relevance of boundary conditions as a new rich source of information about the vacuum structure. In all cases the entropy does not increase along the flow from the ultraviolet to the infrared.
The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective, the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries, this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories, pseudo-periodic and quasi-periodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes, we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. In contrast, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.
The vacuum structure is probed by boundary conditions. The behaviour of thermodynamical quantities such as free energy, boundary entropy and entanglement entropy under the boundary renormalization group flow are analysed in 2D conformal field theories. The results show that wherever vacuum energy and boundary entropy turn out to be very sensitive to boundary conditions, the vacuum entanglement entropy is independent of boundary properties when the boundary of the entanglement domain does not overlap the boundary of the physical space. In all cases the second law of thermodynamics holds along the boundary renormalization group flow.
The vacuum structure is probed by boundary conditions. The behaviour of thermodynamical quantities such as free energy, boundary entropy and entanglement entropy under the boundary renormalization group flow are analysed in 2D conformal field theories. The results show that wherever vacuum energy and boundary entropy turn out to be very sensitive to boundary conditions, the vacuum entanglement entropy is independent of boundary properties when the boundary of the entanglement domain does not overlap the boundary of the physical space. In all cases the second law of thermodynamics holds along the boundary renormalization group flow.
Abstract Spacetime boundaries with canonical Neuman or Dirichlet conditions preserve conformal invarience, but “mixed” boundary conditions which interpolate linearly between them can break conformal symmetry and generate interesting Renormalization Group flows even when a theory is free, providing soluble models with nontrivial scale dependence. We compute the (Rindler) entanglement entropy for a free scalar field with mixed boundary conditions in half Minkowski space and in Anti-de Sitter space. In the latter case we also compute an additional geometric contribution, which according to a recent proposal then collectively give the 1/N corrections to the entanglement entropy of the conformal field theory dual. We obtain some perturbatively exact results in both cases which illustrate monotonic interpolation between ultraviolet and infrared fixed points. This is consistent with recent work on the irreversibility of renormalization group, allowing some assessment of the aforementioned proposal for holographic entanglement entropy and illustrating the generalization of the g-theorem for boundary conformal field theory.
The quantum vacuum is traditionally regarded as a passive backdrop for particle dynamics, yet it is permeated by incessant zero‑point fluctuations that encode the fundamental properties of quantum fields. In this paper we propose a new theoretical construct, termed Vacuum Boundary Information Flow (VBIF), which posits that the boundaries of a vacuum region can act as carriers of information. By modulating the boundary conditions that a quantum field satisfies, one can encode, transmit, and retrieve data through alterations in the vacuum fluctuation spectrum. We develop a rigorous mathematical framework for VBIF, beginning with mode decomposition of a scalar field under general boundary conditions, deriving the transformation laws for field operators when boundary parameters are varied, and quantifying the information capacity of a boundary using entropy measures. The implications of VBIF for quantum communication are explored, including potential for nonlocal information transfer and secure communication protocols that exploit the inherent entanglement of vacuum modes. We discuss the physical limits imposed by relativistic causality and energy conservation, and outline experimental avenues that could probe the feasibility of vacuum‑boundary‑based communication. The VBIF paradigm challenges the conventional notion that the vacuum is inert, opening a new frontier for research into vacuum‑based information processing and quantum technologies.
Quantum many-body systems have a rich structure in the presence of boundaries. We study the ground states of conformal field theories (CFTs) and Lifshitz field theories in the presence of a boundary through the lens of the entanglement entropy. For a family of theories in general dimensions, we relate the universal terms in the entanglement entropy of the bulk theory with the corresponding terms for the theory with a boundary. This relation imposes a condition on certain boundary central charges. For example, in 2+12+12+1 dimensions, we show that the corner-induced logarithmic terms of free CFTs and certain Lifshitz theories are simply related to those that arise when the corner touches the boundary. We test our findings on the lattice, including a numerical implementation of Neumann boundary conditions. We also propose an ansatz, the boundary extensive mutual information model, for a CFT with a boundary whose entanglement entropy is purely geometrical. This model shows the same bulk-boundary connection as Dirac fermions and certain supersymmetric CFTs that have a holographic dual. Finally, we discuss how our results can be generalized to all dimensions as well as to massive quantum field theories.