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On 2-form gauge models of topological phases


Delcamp, Clement; Tiwari, Apoorv (2019). On 2-form gauge models of topological phases. Journal of High Energy Physics, 2019:64.

Abstract

We explore 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space B2G of the symmetry group G, and they are classified by cohomology classes of B2G. For finite symmetry groups, 2-form topological theories have a natural lattice interpretation, which we use to construct a lattice Hamiltonian model in (3+1)d that is exactly solvable. This construction relies on the introduction of a cohomology, dubbed 2-form cohomology, of algebraic cocycles that are identified with the simplicial cocycles of B2G as provided by the so-called W -construction of Eilenberg-MacLane spaces. We show algebraically and geometrically how a 2-form 4-cocycle reduces to the associator and the braiding isomorphisms of a premodular category of G-graded vector spaces. This is used to show the correspondence between our 2-form gauge model and the Walker-Wang model.

Abstract

We explore 2-form topological gauge theories in (3+1)d. These theories can be constructed as sigma models with target space the second classifying space B2G of the symmetry group G, and they are classified by cohomology classes of B2G. For finite symmetry groups, 2-form topological theories have a natural lattice interpretation, which we use to construct a lattice Hamiltonian model in (3+1)d that is exactly solvable. This construction relies on the introduction of a cohomology, dubbed 2-form cohomology, of algebraic cocycles that are identified with the simplicial cocycles of B2G as provided by the so-called W -construction of Eilenberg-MacLane spaces. We show algebraically and geometrically how a 2-form 4-cocycle reduces to the associator and the braiding isomorphisms of a premodular category of G-graded vector spaces. This is used to show the correspondence between our 2-form gauge model and the Walker-Wang model.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Physics Institute
Dewey Decimal Classification:530 Physics
Scopus Subject Areas:Physical Sciences > Nuclear and High Energy Physics
Uncontrolled Keywords:Nuclear and High Energy Physics
Language:English
Date:1 May 2019
Deposited On:13 Jun 2019 15:24
Last Modified:15 Apr 2020 23:46
Publisher:Springer
ISSN:1029-8479
OA Status:Gold
Free access at:Publisher DOI. An embargo period may apply.
Publisher DOI:https://doi.org/10.1007/jhep05(2019)064

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