String condensations in \(3+1\)D and Lagrangian algebras

DOI10.4310/ATMP.2023.V27.N2.A5arXiv2208.07865OpenAlexW4387587800MaRDI QIDQ6080329

Author name not available (Why is that?)

Publication date: 30 October 2023

Published in: (Search for Journal in Brave)

Abstract: We present three Lagrangian algebras in the modular 2-category associated to the 3+1D

m a t h b b Z_{2}

topological order and discuss their physical interpretations, connecting algebras with gapped boundary conditions, and interestingly, maps (braided autoequivalences) exchanging algebras with bulk domain walls. A Lagrangian algebra, together with its modules and local modules, encapsulates detailed physical data of strings condensing at a gapped boundary. In particular, the condensed strings can terminate at boundaries in non-trivial ways. This phenomenon has no lower dimensional analogue and corresponds to novel mathematical structures associated to higher algebras. We provide a layered construction and also explicit lattice realizations of these boundaries and illustrate the correspondence between physics and mathematics of these boundary conditions. This is a first detailed study of the mathematics of Lagrangian algebras in modular 2-categories and their corresponding physics, that brings together rich phenomena of string condensations, gapped boundaries and domain walls in 3+1D topological orders.

Full work available at URL: https://arxiv.org/abs/2208.07865

Mathematics Subject Classification ID

Topological lattices (06B30) Surgery obstructions, Wall groups (57R67) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) String topology (55P50) Braided monoidal categories and ribbon categories (18M15) Particle exchange symmetries in quantum theory (general) (81V72)