Local fields in boundary conformal QFT

TL;DR

This work develops an algebraic framework for boundary conformal QFT on a half-space, showing that BCFT local fields carry a bi-localized product of left and right chiral charges determined by non-local chiral extensions of a completely rational chiral net $A$. By formulating BCFT as a boundary net induced from a chiral extension and connecting it to 2D Minkowski-space theories via $ ext{alpha}$-induction, the authors establish isomorphisms between local subfactors in boundary and bulk theories and describe charged intertwiners that realize the bi-local charge structure. They prove that varying the non-local chiral extension within a DHR orbit yields a family of locally isomorphic BCFTs with a nimrep controlling boundary multiplicities and partition functions, linking boundary conditions to the DHR category data. The analysis clarifies Cardy-type factorization of correlation functions as a universal consequence of the algebraic structure, independent of diffeomorphism invariance, and lays out how modular invariants arise from the underlying braided tensor category. Overall, the paper provides a comprehensive algebraic classification of BCFTs via Q-systems, relating boundary phenomena to bulk CFT data and modular structure while highlighting the bi-localized charge content of boundary fields.

Abstract

Conformal field theory on the half-space x>0 of Minkowski space-time ("boundary CFT") is analyzed from an algebraic point of view, clarifying in particular the algebraic structure of local algebras and the bi-localized charge structure of local fields. The field content and the admissible boundary conditions are characterized in terms of a non-local chiral field algebra.