Abstract
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 B
2
G of the symmetry group G, and they are classified by cohomology classes of B
2
G. 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 B
2
G 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.
Publisher
Springer Science and Business Media LLC
Subject
Nuclear and High Energy Physics
Reference104 articles.
1. M. Atiyah, Topological quantum field theories, Inst. Hautes Etudes Sci. Publ. Math.
68 (1989) 175 [INSPIRE].
2. J.C. Baez and J. Dolan, Higher dimensional algebra and topological quantum field theory, J. Math. Phys.
36 (1995) 6073 [q-alg/9503002] [INSPIRE].
3. J. Lurie, Higher topos theory, Princeton University Press, Princeton U.S.A. (2009).
4. J. Lurie, On the classification of topological field theories, arXiv:0905.0465 [INSPIRE].
5. D.S. Freed, The cobordism hypothesis, arXiv:1210.5100 [INSPIRE].
Cited by
21 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献