Entropic C-theorems in free and interacting two-dimensional field theories

Details Entropic C-theorems in free and interacting two-dimensional field theories Entropic C-theorems in free and interacting two-dimensional field theories

1998-10-14

arxiv.org/abs/hep-th/9810107v2

Phys.Rev.D61:045006,2000

Physics

High Energy Physics

High Energy Physics - Theory

34 pages, 3 figures (8 EPS files), Latex2e file, continuation of hep-th/9710241; rigorous analysis of sufficient conditions fo

Scientific paper

10.1103/PhysRevD.61.045006

The relative entropy in two-dimensional field theory is studied on a cylinder geometry, interpreted as finite-temperature field theory. The width of the cylinder provides an infrared scale that allows us to define a dimensionless relative entropy analogous to Zamolodchikov's $c$ function. The one-dimensional quantum thermodynamic entropy gives rise to another monotonic dimensionless quantity. I illustrate these monotonicity theorems with examples ranging from free field theories to interacting models soluble with the thermodynamic Bethe ansatz. Both dimensionless entropies are explicitly shown to be monotonic in the examples that we analyze.

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