Duality and defects in rational conformal field theory
Jürg Fröhlich, Jürgen Fuchs, Ingo Runkel, Christoph Schweigert
TL;DR
Fröhlich, Fuchs, Runkel, and Schweigert develop a TFT-based, category-theoretic framework for topological defect lines in 2D rational conformal field theories. They identify internal CFT symmetries with the Picard group of A-bimodules in a modular tensor category and show that Morita equivalence classes of symmetric special Frobenius algebras label the same full CFT on oriented worldsheets. The work introduces and characterizes group-like defects as symmetry generators and duality defects as engines of order-disorder dualities, with a non-degeneracy result ensuring distinct defects yield distinct bulk-field actions. The paper provides a concrete demonstration in the c=4/5 tetracritical Ising vs Potts models, where defect fusion realizes an S3 symmetry and phase-changing defects connect different world-sheet phases via orbifold-like relations. It also lays out the TFT calculus for defect correlators and discusses unoriented extensions and simple-current theories, broadening the applicability of RCFT defect analysis.
Abstract
We study topological defect lines in two-dimensional rational conformal field theory. Continuous variation of the location of such a defect does not change the value of a correlator. Defects separating different phases of local CFTs with the same chiral symmetry are included in our discussion. We show how the resulting one-dimensional phase boundaries can be used to extract symmetries and order-disorder dualities of the CFT. The case of central charge c=4/5, for which there are two inequivalent world sheet phases corresponding to the tetra-critical Ising model and the critical three-states Potts model, is treated as an illustrative example.