Geometric modular action for disjoint intervals and boundary conformal field theory

TL;DR

This paper explores how the modular group acts geometrically in boundary conformal quantum field theory, relating temperature and acceleration, and discusses phenomena like mixing and charge splitting in disjoint intervals.

Contribution

It extends the understanding of geometric modular action from chiral conformal QFT to boundary conformal QFT, revealing new relations between temperature and acceleration.

Findings

Modular group acts geometrically in boundary conformal QFT.

Relation established between temperature and acceleration.

Discussion of mixing and charge splitting phenomena.

Abstract

In suitable states, the modular group of local algebras associated with unions of disjoint intervals in chiral conformal quantum field theory acts geometrically. We translate this result into the setting of boundary conformal QFT and interpret it as a relation between temperature and acceleration. We also discuss aspects ("mixing" and "charge splitting") of geometric modular action for unions of disjoint intervals in the vacuum state.