Phase boundaries in algebraic conformal QFT

TL;DR

This paper analyzes the structure of local algebras in conformal quantum field theory with phase boundaries, classifying boundary conditions through algebraic methods rooted in Einstein Causality.

Contribution

It introduces a universal algebraic framework to classify phase boundary conditions in conformal QFT, connecting with previous results.

Findings

Classification of phase boundary conditions via the centre of a universal algebraic construction.

Reproduction of known results in a broad class of models.

Framework emphasizes the role of Einstein Causality in boundary algebra structures.

Abstract

We study the structure of local algebras in relativistic conformal quantum field theory with phase boundaries. Phase boundaries are instances of a more general notion of boundaries that give rise to a variety of algebraic structures. These can be formulated in a common framework originating in Algebraic QFT, with the principle of Einstein Causality playing a prominent role.We classify the phase boundary conditions by the centre of a certain universal construction, which produces a reducible representation in which all possible boundary conditions are realized. For a large class of models, the classification reproduces results obtained in a different approach by Fuchs et al. before.