# Irreversibility in quantum field theories with boundaries

## TL;DR

This paper investigates the irreversibility of boundary renormalization group flows in conformal field theories using quantum information theory, extending entropic theorems to higher dimensions and providing new bounds and sum rules.

## Contribution

It generalizes the entropic g-theorem to higher dimensions, proves the entropic b-theorem in 2+1 dimensions, and introduces a sum rule for boundary effects in quantum field theories.

## Key findings

- Positivity of relative entropy bounds boundary RG flows.
- The entropic b-theorem shows the Weyl anomaly decreases under boundary RG flows.
- A sum rule for the change in the boundary area term is established.

## Abstract

We study conformal field theories with boundaries, and their boundary renormalization group (RG) flows, using methods from quantum information theory. Positivity of the relative entropy, together with unitarity and Lorentz invariance, give rise to bounds that characterize the irreversibility of such flows. This generalizes the recently proved entropic $g$-theorem to higher dimensions. In $2+1$ dimensions with a boundary, we prove the entropic $b$-theorem -- the decrease of the two-dimensional Weyl anomaly under boundary RG flows. In higher dimensions, the bound implies that the leading area coefficient of the entanglement entropy induced by the defect decreases along the flow. Our proof unifies these properties, and provides an information-theoretic interpretation in terms of the distinguishability between the short distance and long distance states. Finally, we establish a sum rule for the change in the area term in theories with boundaries, which could have implications for models with localized gravity.