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

TL;DR

This paper explores entropic quantities in two-dimensional quantum field theories on a cylinder, establishing monotonicity theorems that extend concepts like the c-theorem to both free and interacting models.

Contribution

It introduces and proves entropic C-theorems in 2D field theories, connecting relative entropy and thermodynamic entropy with monotonic behavior across different models.

Findings

Both entropic measures are shown to be monotonic in analyzed examples.

The dimensionless relative entropy generalizes the c-theorem.

Thermodynamic entropy provides an additional monotonic quantity.

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.