1999/11/15 by José Gaite, Jose Gaite
Mathematics · Physics and Astronomy · #Asymptotic expansion #Black Holes and Theoretical Physics #Compact Riemann surface #Conformal map #Constant curvature #Cosmology and Gravitation Theories #Curvature #Geometry #Logarithm #Mathematical analysis #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Riemann surface #Series (stratigraphy) #Torus #cond-mat.stat-mech #gr-qc #hep-th
paper · pdf · doi:10.1103/physrevd.61.084001
published as Phys.Rev.D61:084001,2000 · 20 pages, LaTeX 2e, 2 PS figures; to appear in Phys. Rev. D
arxiv created 1999/11/15 · openalex publication_date 2000/03/13 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The relative entropy of the massive free bosonic field theory is studied on various compact Riemann surfaces as a universal quantity with physical significance, in particular, for gravitational phenomena. The exact expression for the sphere is obtained, as well as its asymptotic series for large mass and its Taylor series for small mass. One can also derive exact expressions for the torus but not for higher genus. However, the asymptotic behavior for large mass can always be established---up to a constant---with heat-kernel methods. It consists of an asymptotic series determined only by the curvature---and, hence, is common for homogeneous surfaces of genus higher than one---and exponentially vanishing corrections whose form is determined by the concrete topology. The coefficient of the logarithmic term in this series gives the conformal anomaly.