2007/04/09 by M. Asorey, D. García-Álvarez, D. Garcia-Alvarez +2 · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Boundary conformal field theory #Boundary value problem #Cosmology and Gravitation Theories #Dirichlet boundary condition #Fixed point #Infrared fixed point #Invariant (physics) #Mathematical analysis #Mathematical physics #Mathematics #Mixed boundary condition #Neumann boundary condition #Physics #Quantum #Quantum Electrodynamics and Casimir Effect #Quantum entanglement #Quantum field theory #Quantum gravity #Quantum mechanics #Renormalization #Renormalization group #Robin boundary condition #Thermal quantum field theory #Ultraviolet fixed point #Vacuum energy #hep-th
paper · pdf · doi:10.1088/1751-8113/40/25/s21
published as J.Phys.A40:6767-6776,2007 · 10 pages, 1 eps figure
arxiv created 2007/04/09 · openalex publication_date 2007/06/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.