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

Abstract

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.

34 pages, 3 figures (8 EPS files), Latex2e file, continuation of hep-th/9710241; rigorous analysis of sufficient conditions for universality of the dimensionless relative entropy, more detailed discussion of the relation with Zamolodchikov's theorem, references added; to appear in Phys. Rev. D

References in corpus (4)

• Exclusion Statistics in Conformal Field Theory Spectra
• Thermodynamic Bethe Ansatz with Haldane Statistics
• Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group
• On thermodynamic approaches to conformal field theory

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• Renormalization group irreversible functions in more than two dimensions
• Quasi-particle re-summation and integral gap equation in thermal field theory
• Relative entropy for compact Riemann surfaces