Defects and Bulk Perturbations of Boundary Landau-Ginzburg Orbifolds

TL;DR

This work develops a non-perturbative framework to study bulk perturbations and their induced boundary RG flows by introducing defect lines that connect UV and IR CFTs. Focusing on supersymmetric flows between minimal model orbifolds, it constructs B-type defects in Landau-Ginzburg orbifolds via $\Gamma$-equivariant matrix factorisations and analyzes their fusion with both other defects and B-type boundaries. A central contribution is a special class of defects $P^{(m,n)}$ between $X^{d}/\mathbb{Z}_d$ and $X^{d'}/\mathbb{Z}_{d'}$, with explicit fusion rules and boundary-action formulas that reproduce the expected boundary flows, corroborated by mirror symmetry via A-branes and Lefschetz pencils. The results illuminate a robust, non-perturbative mechanism for tracing bulk-boundary RG flows and point to natural extensions to affine orbifolds and multi-field Landau-Ginzburg models, where similar defect constructions may govern boundary dynamics.

Abstract

We propose defect lines as a useful tool to study bulk perturbations of conformal field theories, in particular to analyse the induced renormalisation group flows of boundary conditions. As a concrete example we investigate bulk perturbations of N=2 supersymmetric minimal models. To these perturbations we associate a special class of defects between the respective UV and IR theories, whose fusion with boundary conditions indeed reproduces the behaviour of the latter under the corresponding RG flows. v2: Some explanations added in section 4, minor changes.