Relative entropy in 2d Quantum Field Theory, finite-size corrections and irreversibility of the Renormalization Group

TL;DR

This paper explores the use of relative entropy in 2D quantum field theory as an irreversible measure under the Renormalization Group, establishing connections with thermodynamic entropy and proposing entropic c theorems as analogues of Zamolodchikov's c theorem.

Contribution

It introduces a new application of relative entropy as an irreversible quantity in 2D QFT and relates it to thermodynamic entropy and stress tensor components.

Findings

Relative entropy defines a monotonic quantity similar to the c function.

Thermodynamic entropy also yields a monotonic quantity with distinct properties.

Entropic c theorems are proposed as analogues of Zamolodchikov's c theorem.

Abstract

The relative entropy in two-dimensional Field Theory is studied for its application as an irreversible quantity under the Renormalization Group, relying on a general monotonicity theorem for that quantity previously established. In the cylinder geometry, interpreted as finite-temperature field theory, one can define from the relative entropy a monotonic quantity similar to Zamolodchikov's c function. On the other hand, the one-dimensional quantum thermodynamic entropy also leads to a monotonic quantity, with different properties. The relation of thermodynamic quantities with the complex components of the stress tensor is also established and hence the entropic c theorems are proposed as analogues of Zamolodchikov's c theorem for the cylinder geometry.