Symmetry breaking boundaries II. More structures; examples

TL;DR

This paper explores the mathematical structures of symmetry breaking boundary conditions in orbifold conformal field theories, introducing new classifications, algebraic tools, and applications such as non-BPS boundary conditions in string theory.

Contribution

It establishes the properties and classifications of symmetry breaking boundary conditions, introduces a classifying algebra, and demonstrates applications in string theory.

Findings

Correlation functions are expressible via twisted boundary blocks.

Boundary conditions sharing the same automorphism type are controlled by a classifying algebra.

T-duality on boundary conditions is generally not one-to-one.

Abstract

Various structural properties of the space of symmetry breaking boundary conditions that preserve an orbifold subalgebra are established. To each such boundary condition we associate its automorphism type. It is shown that correlation functions in the presence of such boundary conditions are expressible in terms of twisted boundary blocks which obey twisted Ward identities. The subset of boundary conditions that share the same automorphism type is controlled by a classifying algebra, whose structure constants are shown to be traces on spaces of chiral blocks. T-duality on boundary conditions is not a one-to-one map in general. These structures are illustrated in a number of examples. Several applications, including the construction of non-BPS boundary conditions in string theory, are exhibited.