Tensor network approach to electromagnetic duality in (3+1)d topological gauge models

A bstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G , we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical f...

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Bibliographic Details
Published in:The journal of high energy physics 2022-08, Vol.2022 (8), p.149-39, Article 149
Main Author: Delcamp, Clement
Format: Article
Language:English
Subjects:
Boundary conditions
Classical and Quantum Gravitation
Dirichlet problem
Duality in Gauge Field Theories
Elementary Particles
Entanglement
Gauge Symmetry
Gauge theory
Hamiltonian functions
High energy physics
Ising model
Mathematical analysis
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Quantum Physics
Regular Article - Theoretical Physics
Relativity Theory
Representations
String Theory
Symmetry
Tensors
Topological States of Matter
Topology
Vector spaces
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Summary:A bstract Given the Hamiltonian realisation of a topological (3+1)d gauge theory with finite group G , we consider a family of tensor network representations of its ground state subspace. This family is indexed by gapped boundary conditions encoded into module 2-categories over the input spherical fusion 2-category. Individual tensors are characterised by symmetry conditions with respect to non-local operators acting on entanglement degrees of freedom. In the case of Dirichlet and Neumann boundary conditions, we show that the symmetry operators form the fusion 2-categories 2Vec G of G -graded 2-vector spaces and 2Rep( G ) of 2-representations of G , respectively. In virtue of the Morita equivalence between 2Vec G and 2Rep( G ) — which we explicitly establish — the topological order can be realised as the Drinfel’d centre of either 2-category of operators; this is a realisation of the electromagnetic duality of the theory. Specialising to the case G = ℤ 2 , we recover tensor network representations that were recently introduced, as well as the relation between the electromagnetic duality of a pure ℤ 2 gauge theory and the Kramers-Wannier duality of a boundary Ising model.
ISSN:1029-8479
1029-8479
DOI:10.1007/JHEP08(2022)149