Domain walls between 3d phases of Reshetikhin-Turaev TQFTs

TL;DR

This paper develops a new explicit construction for surface defects in 3D Reshetikhin-Turaev TQFTs, generalizing previous models and confirming consistency with existing theoretical frameworks.

Contribution

It introduces a novel Frobenius algebra framework over two commutative Frobenius algebras for constructing surface defects in 3D TQFTs, extending prior models.

Findings

Explicit, computable construction of surface defects.

Specialization to known models when all 3-strata are identical.

Agreement with existing model-independent analyses.

Abstract

We study surface defects in three-dimensional topological quantum field theories which separate different theories of Reshetikhin-Turaev type. Based on the new notion of a Frobenius algebra over two commutative Frobenius algebras, we present an explicit and computable construction of such defects. It specialises to the construction in Carqueville et al., arXiv:1710.10214 if all 3-strata are labelled by the same topological field theory. We compare the results to the model-independent analysis in Fuchs et al., arXiv:1203.4568 and find agreement.