Defect Lines and Boundary Flows

TL;DR

The paper derives a general rule for boundary RG flows in rational CFTs using defect lines: if a flow $b \to d$ exists, then a corresponding flow $a \times b \to a \times d$ exists. This embedding is established via an algebraic construction of defect lines that map the boundary sector of $b$ into the boundary sector of $a \times b$, yielding exact results independent of numerics. The authors apply the theorem to minimal models and coset theories, recovering and extending known flows and providing a framework to reduce more complex conjectures to elementary, verifiable flows. The work highlights how defect-line techniques unify and extend boundary-flow analyses, with potential extensions to non-diagonal RCFTs and topological quantum field theory formalisms.

Abstract

Using the properties of defect lines, we study boundary renormalisation group flows. We find that when there exists a flow between maximally symmetric boundary conditions "a" and "b" then there also exists a boundary flow between "c x a" and "c x b" where "x" denotes the fusion product. We also discuss applications of this simple observation.

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