Higher obstructions to conformal boundary conditions and lattice realizations

TL;DR

This paper investigates higher obstructions, called higher central charges, that prevent certain 2d rational CFTs with vanishing chiral central charges from having conformal boundary conditions, impacting lattice models and symmetries.

Contribution

It identifies and analyzes higher central charges as obstructions to conformal boundary conditions in 2d rational CFTs, extending understanding beyond traditional central charge considerations.

Findings

Higher central charges serve as obstructions to boundary conditions.

Implications for lattice realizations of 2d rational CFTs.

Discussion on generalizations involving global symmetries.

Abstract

Although it is long believed that vanishing of chiral central charges of a 2d conformal field theory (CFT) implies the existence of conformal boundary conditions, there are yet higher obstructions. In this paper, we focus on 2d rational CFTs, for which we identify a series of obstructions, known as higher central charges. We also discuss its implication for lattice realizations and the generalization with global symmetries.