3-form Yang-Mills based on 2-crossed modules

Song, Danhua; Wu, Ke; Yang, Jie

doi:10.1016/j.geomphys.2022.104537

Cited by 4 publications

(4 citation statements)

References 25 publications

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“…Based on these higher gauge theories, the electromagnetic theory has been generalized to the p-form electromagnetic theory [26][27][28]. Likewise, the Yang-Mills (YM) theory has been generalized to the 2-form Yang-Mills (2YM) theory [29] and the 3-form Yang-Mills (3YM) theory [30], respectively. Furthermore, the topological BF theory has been generalized to the topological 2BF [31][32][33][34][35][36] and 3BF theories [37][38][39].…”

Section: Jhep07(2023)207mentioning

confidence: 99%

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Higher Chern-Simons based on (2-)crossed modules

Song

et al. 2023

J. High Energ. Phys.

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We present higher Chern-Simons theories based on (2-)crossed modules. We start from the generalized differential forms in Generalized Differential Calculus and define the corresponding generalized connections which consist of higher connections. Then we establish the generalized Chern-Simons forms to get the higher Chern-Simons actions. Finally, we develop the higher second Chern forms and Chern-Weil theorems.

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Section: Jhep07(2023)207mentioning

confidence: 99%

“…For a rigorous derivation of these identities, the reader is referred to [30]. Without loss of generality, we consider three kinds of 3-gauge transformations from a 3-connection (A, B, C) to another one (A , B , C ):…”

Section: -Connections and 3-gauge Transformationsmentioning

confidence: 99%

Higher Chern-Simons based on (2-)crossed modules

Song

et al. 2023

J. High Energ. Phys.

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“…In some of the modern approaches to the problem of quantum gravity based on the spinfoam formalism of loop quantum gravity [13,14], as well as in other applications of the so-called higher gauge theory (see [15] for a review and [16] for an application to quantum gravity), the description of gauge symmetry is being extended from the notion of a Lie group to different algebraic structures, called 2-groups, 3-groups, and in general, n-groups [17][18][19][20][21][22][23][24][25][26][27]. In this context, it is important to revisit and study the specific class of HT gauge symmetries, since they provide a nontrivial insight into the properties of these more general algebraic structures, as well as the physics behind the symmetries they describe.…”

Section: Introductionmentioning

confidence: 99%

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

et al. 2023

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When discussing the gauge symmetries of any theory, the Henneaux–Teitelboim transformations are often underappreciated or even completely ignored, due to their on-shell triviality. Nevertheless, these gauge transformations play an important role in understanding the structure of the full gauge symmetry group of any theory, especially regarding the subgroup of diffeomorphisms. We give a review of the Henneaux–Teitelboim transformations and the resulting gauge group in the general case and then discuss its role in the applications to the class of topological theories called nBF models, relevant for the constructions of higher gauge theories and quantum gravity.

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“…In order to overcome this problem, a new approach has been developed within the framework of higher gauge theory (for a review of higher gauge theory, see [16,17], and for its applications in physics see [18][19][20][21][22][23][24][25][26][27][28][29]). Within higher gauge theory formalism, one generalizes the BF action, based on some Lie group, to an 2BF action based on the 2-group structure.…”

Section: Introductionmentioning

confidence: 99%

Topological invariant of 4-manifolds based on a 3-group

Radenkovic

Vojinović

2022

J. High Energ. Phys.

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We study a generalization of 4-dimensional BF-theory in the context of higher gauge theory. We construct a triangulation independent topological state sum Z, based on the classical 3BF action for a general 3-group and a 4-dimensional spacetime manifold $$ \mathcal{M} $$ M 4. This state sum coincides with Porter’s TQFT for d = 4 and n = 3. In order to verify that the constructed state sum is a topological invariant of the underlying 4-dimensional manifold, its behavior under Pachner moves is analyzed, and it is obtained that the state sum Z remains the same. This paper is a generalization of the work done by Girelli, Pfeiffer, and Popescu for the case of state sum based on the classical 2BF action with the underlying 2-group structure.

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3-form Yang-Mills based on 2-crossed modules

Cited by 4 publications

References 25 publications

Higher Chern-Simons based on (2-)crossed modules

Higher Chern-Simons based on (2-)crossed modules

Henneaux–Teitelboim Gauge Symmetry and Its Applications to Higher Gauge Theories

Topological invariant of 4-manifolds based on a 3-group

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