Associativity of branchwise classical defect fusion

Establish associativity of the classical target-space fusion prescription, including the subsequent selection of admissible branches and descent of connection data, and determine whether these operations are independent of the order of fusion.

Background

The paper defines classical fusion by composing defect supports via a fibre product, combining their intrinsic two-forms and connection data, restricting to loci where these data descend through projection, and retaining branches satisfying the topologicality conditions. Although the initial composition of defect supports is associative up to a natural identification, the later branch-selection and connection-descent steps may introduce order dependence. The authors therefore explicitly identify associativity of the complete prescription as unresolved.

References

It also remains to establish associativity. Although the initial composition of the defect supports is associative up to a natural identification, the subsequent selection of admissible branches and descent of the connection data may actually depend on the order of fusion.

— Target-space fusion of classical topological defects  (2608.21121 - Demulder et al., 21 Aug 2026) in Section 5, “Summary and conclusions,” paragraph “Singular branches and associativity”