Higher form Yang-Mills as higher BFYM theories

Song, Danhua; Lou, Kai; Wu, Ke; Yang, Jie

doi:10.48550/arxiv.2109.13443

Cited by 4 publications

(10 citation statements)

References 49 publications

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“…See Appendix A for more details. The definitions and properties of the ordinary differential forms with values in differential (2-)crossed module have been introduced in our previous paper [33] and related work [21]. We shall give a small taste of these reviews to the literature, seeing more details in Appendix B.…”

Section: Generalized Forms Valued In Differential Crossed Module and ...mentioning

confidence: 99%

“…We will pay our attention to the case when the base group G is compact in the real case, or has a compact real form in the complex case, so that G-invariant non-degenerate bilinear forms in g, h and l will always exist [29,33]. From these invariance conditions, one immediately sees that…”

Section: Generalized G-invariant Bilinear Formsmentioning

confidence: 99%

“…See [28] for more properties of those maps. And most of the conventions of reference [33] are retained.…”

Section: Generalized G-invariant Bilinear Formsmentioning

confidence: 99%

“…Review the notion of ordinary 3-connection in [33]. Let (L, H, G; β, α, ⊲, {, }) be a Lie 2-crossed module.…”

Section: Generalized 3-connectionsmentioning

confidence: 99%

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Generalized higher connections and Yang-Mills

Song¹,

Lou²,

Wu³

et al. 2021

Preprint

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We first extend Generalized Differential Calculus (GDC) to higher structures and create generalized G-invariant bilinear forms. In addition, we also focus on developing generalized 2-and 3-connection theories in the framework of GDC. Then, we derive the higher Bianchi-Identities and study the gauge transformations for those generalized higher connections. Finally, we establish the generalized 2-and 3-form Yang-Mills theories based on GDC and obtain the corresponding fields equations.

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Section: Generalized Forms Valued In Differential Crossed Module and ...mentioning

confidence: 99%

Section: Generalized G-invariant Bilinear Formsmentioning

confidence: 99%

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Generalized higher connections and Yang-Mills

Song¹,

Lou²,

Wu³

et al. 2021

Preprint

Self Cite

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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, which is based on some Lie group, to a 2BF action based on the 2-group structure.…”

Section: Introductionmentioning

confidence: 99%

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

Radenkovic,

Vojinovic

2022

Preprint

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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 M4. 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 the 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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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.

show abstract

Higher form Yang-Mills as higher BFYM theories

Cited by 4 publications

References 49 publications

Generalized higher connections and Yang-Mills

Generalized higher connections and Yang-Mills

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

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

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