Topological higher gauge theory: From BF to BFCG theory

Girelli, Florian; Pfeiffer, Hendryk; Popescu, E. M.

doi:10.1063/1.2888764

Cited by 58 publications

(90 citation statements)

References 24 publications

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“…Using these variables, one can introduce a new action as a generalization of the BF action, such that it is gauge invariant with respect to both G and H groups. It is called the 2BF action and is defined in the following way [16,17]:…”

Section: Bf Theorymentioning

confidence: 99%

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Higher gauge theories based on 3-groups

Radenkovic

Vojinović

2019

J. High Energ. Phys.

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We study the categorical generalizations of a BF theory to 2BF and 3BF theories, corresponding to 2-groups and 3-groups, in the framework of higher gauge theory. In particular, we construct the constrained 3BF actions describing the correct dynamics of Yang-Mills, Klein-Gordon, Dirac, Weyl, and Majorana fields coupled to Einstein-Cartan gravity. The action is naturally split into a topological sector and a sector with simplicity constraints, adapted to the spinfoam quantization programme. In addition, the structure of the 3-group gives rise to a novel gauge group which specifies the spectrum of matter fields present in the theory, just like the ordinary gauge group specifies the spectrum of gauge bosons in the Yang-Mills theory. This allows us to rewrite the whole Standard Model coupled to gravity as a constrained 3BF action, facilitating the nonperturbative quantization of both gravity and matter fields. Moreover, the presence and the properties of this new gauge group open up a possibility of a nontrivial unification of all fields and a possible explanation of fermion families and all other structure in the matter spectrum of the theory.

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Section: Bf Theorymentioning

confidence: 99%

“…2 BF and 2BF models, ordinary gauge fields and gravity Let us begin by giving a short review of BF and 2BF theories in general. For additional information on these topics, see for example [11,[13][14][15][16][17][18]].…”

Section: Introductionmentioning

confidence: 99%

Higher gauge theories based on 3-groups

Radenkovic

Vojinović

2019

J. High Energ. Phys.

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“…(4d) In four dimensions, a similar argument to that just made in three dimensions leads to a class of dual models that are "higher-gauge theories" [80,81]: the variables are associated to the faces of the dual lattice, and the weights define couplings among the faces bounding three-dimensional cells.…”

Section: Dual Modelsmentioning

confidence: 99%

Spin Foam Models with Finite Groups

2013

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Spin foam models, loop quantum gravity, and group field theory are discussed as quantum gravity candidate theories and usually involve a continuous Lie group. We advocate here to consider quantum gravity-inspired models with finite groups, firstly as a test bed for the full theory and secondly as a class of new lattice theories possibly featuring an analogue diffeomorphism symmetry. To make these notes accessible to readers outside the quantum gravity community, we provide an introduction to some essential concepts in the loop quantum gravity, spin foam, and group field theory approach and point out the many connections to the lattice field theory and the condensed-matter systems.

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“…We infer that a naturally generalized setup in which BF theory should be considered, is a Lie 2-group G, i.e., a smooth crossed module (G, H, t, α), together with the invariant form −, − on the Lie algebra of G. Other generalizations have been proposed in [GPP08]. The fields are now pairs (A, B) of a 1-form A ∈ Ω 1 (X, g) and a 2-form B ∈ Ω 2 (X, h), and the action is, with…”

Section: Classical Solutions In Bf-theorymentioning

confidence: 99%

Smooth functors vs. differential forms

Schreiber

Waldorf

2011

Homology, Homotopy and Applications

153

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We establish a relation between smooth 2-functors defined on the path 2-groupoid of a smooth manifold and differential forms on this manifold. This relation can be understood as a part of a dictionary between fundamental notions from category theory and differential geometry. We show that smooth 2-functors appear in several fields, namely as connections on (non-abelian) gerbes, as derivatives of smooth functors and as critical points in BF theory. We demonstrate further that our dictionary provides a powerful tool to discuss the transgression of geometric objects to loop spaces.

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Topological higher gauge theory: From BF to BFCG theory

Cited by 58 publications

References 24 publications

Higher gauge theories based on 3-groups

Higher gauge theories based on 3-groups

Spin Foam Models with Finite Groups

Smooth functors vs. differential forms

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