Higher lattice gauge theory from representations of 2-groups and 3+1D topological phases

2025/12/22 by Latévi M. Lawson, Lawson, Latévi M., Prince K. Osei +1
Physics and Astronomy · #Quantum many-body systems #Quantum Chromodynamics and Particle Interactions #Topological Materials and Phenomena

paper · doi:10.48550/arxiv.2512.19608

Abstract

We construct a higher lattice gauge theory based on the representation of 2-groups described by a category of crossed modules on a lattice model described by path 2-groupoids. Using these lattice gauge representations, an exactly solvable Hamiltonian for topological phases in 3+1 dimensions is constructed. We show that the ground states of this model are topological observables.

Citations

• Ribbon operators in the Semidual lattice code model
• Algebraic Aspects of Boundaries in the Kitaev Quantum Double Model
• Group field theory on 2-groups
• Study of a lattice 2-group gauge model
• Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras
• Defects in Kitaev models and bicomodule algebras
• Semidual Kitaev lattice model and tensor network representation
• Transformation Double Categories Associated to 2-Group Actions
• Kitaev's Lattice Model and Turaev-Viro TQFTs
• (3+1)-TQFTs and Topological Insulators
• Higher Gauge Theory
• Topological quantum memory
• A modular functor which is universal for quantum computation
• Fault-tolerant quantum computation by anyons

Related

• Higher symmetry and gapped phases of gauge theories
• Study of a lattice 2-group gauge model
• Topological Order from a Cohomological and Higher Gauge Theory perspective
• Finite 2-group gauge theory and its 3+1D lattice realization
• Exactly solvable models for 2+1D topological phases derived from crossed modules of semisimple Hopf algebras