Relative entropy for compact Riemann surfaces

Details Relative entropy for compact Riemann surfaces Relative entropy for compact Riemann surfaces

1999-11-15

arxiv.org/abs/hep-th/9911111v1

Phys.Rev.D61:084001,2000

Physics

High Energy Physics

High Energy Physics - Theory

20 pages, LaTeX 2e, 2 PS figures; to appear in Phys. Rev. D

Scientific paper

10.1103/PhysRevD.61.084001

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 behaviour 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, hence 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.

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