A note on permutation twist defects in topological bilayer phases

Abstract

We present a mathematical derivation of some of the most important physical quantities arising in topological bilayer systems with permutation twist defects as introduced by Barkeshli et al. in cond-mat/1208.4834. A crucial tool is the theory of permutation equivariant modular functors developed by Barmeier et al. in math.CT/0812.0986 and math.QA/1004.1825.

18 pages, some figures

References in corpus (3)

• Topological boundary conditions in abelian Chern-Simons theory
• Morita classes of algebras in modular tensor categories
• A geometric approach to boundaries and surface defects in Dijkgraaf-Witten theories

Cited by in corpus (9)

• Boundary-bulk relation in topological orders
• On Gauging Symmetry of Modular Categories
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Matrix product operator symmetries and intertwiners in string-nets with domain walls
• Gapless edges of 2d topological orders and enriched monoidal categories
• Orbifolds of n-dimensional defect TQFTs
• 3-dimensional defect TQFTs and their tricategories
• Exotic Non-Abelian Topological Defects in Lattice Fractional Quantum Hall States
• Fractional quantum Hall states with gapped boundaries in an extreme lattice limit