Topological defects in open string field theory

TL;DR

This work demonstrates that topological defects from boundary conformal field theory induce open-string defect operators that map OSFT solutions between BCFTs, linking boundary data and bulk fusion through a consistent algebraic and geometric framework. It provides two complementary derivations (algebraic and defect-network based) showing that open defect fusion reproduces the bulk fusion algebra up to a similarity transformation in Chan-Paton space, governed by Racah/6J data. The approach is validated in diagonal minimal models and illustrated explicitly in the Ising model OSFT, where defect actions on boundary fields and classical solutions are computed and matched with BCFT expectations. By connecting OSFT observables (S and Ellwood invariants) and boundary states under defect action (KMS/KOZ), the paper offers a principled mechanism to generate new D-brane configurations and relate BCFT data across theories with potential applications to broader RCFTs and non-rational CFTs.

Abstract

We show how conformal field theory topological defects can relate solutions of open string field theory for different boundary conditions. To this end we generalize the results of Graham and Watts to include the action of defects on boundary condition changing fields. Special care is devoted to the general case when nontrivial multiplicities arise upon defect action. Surprisingly the fusion algebra of defects is realized on open string fields only up to a (star algebra) isomorphism.

Figures (23)

• Figure 1: Action of the topological defect on a boundary field $\phi_i^{ab}$ can be described by enclosing it with an open defect attached to the boundary. The result is a collection (direct sum) of boundary fields $\phi_i^{a'b'}$ in all possible new boundary conditions allowed by fusion. The dots at the junctions represent simple normalization factors determined in subsection \ref{['subsec:geom_constr']}.
• Figure 2: The topological nature of defects implies that an"s-channel" configuration with an elementary defect should be equivalent to a "t-channel" configuration with a composite, but still topological defect.
• Figure 3: Elementary defect network move.
• Figure 4: Pentagon identity as a consistency condition for fusion of defects.
• Figure 5: Defect bubble network. When no operators are present inside, the topological bubble can be shrank to zero size, yielding a numerical factor symmetric under the exchange of $a$ and $b$ labels.