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

Radenkovic, Tijana; Vojinović, Marko

doi:10.1007/jhep07(2022)105

Cited by 4 publications

(7 citation statements)

References 51 publications

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“…These results complete the first step of the spinfoam quantization programme, as outlined in the Introduction. The second step has also been performed in [25], for a general case of a invariant of a 4-dimensional manifold, and has the following form:…”

Section: Discussionmentioning

confidence: 99%

Higher category theory and n-groups as gauge symmetries for quantum gravity

Nikolić,

Obrić,

Radenković

et al. 2023

J. Phys.: Conf. Ser.

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Higher category theory can be employed to generalize the notion of a gauge group to the notion of a gauge n-group. This novel algebraic structure is designed to generalize notions of connection, parallel transport and holonomy from curves to manifolds of dimension higher than one. Thus it generalizes the concept of gauge symmetry, giving rise to a topological action called nBF action, living on a corresponding n-principal bundle over a spacetime manifold. Similarly as for the Plebanski action, one can deform the topological nBF action by adding appropriate simplicity constraints, in order to describe the correct dynamics of both gravity and matter fields. Specifically, one can describe the whole Standard Model coupled to gravity as a constrained 3BF or 4BF action. The split of the full action into a topological sector and simplicity constraints sector is adapted to the spinfoam quantization technique, with the aim to construct a full model of quantum gravity with matter. In addition, the properties of the gauge n-group structure open up a possibility of a nontrivial unification of all fields. An n-group naturally contains additional novel gauge groups which specify the spectrum of matter fields present in the theory, in a similar way to the ordinary gauge group that prescribes the spectrum of gauge vector bosons in the Yang-Mills theory. The presence and the properties of these new gauge groups has the potential to explain fermion families, and other structure in the matter spectrum of the theory.

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Section: Discussionmentioning

confidence: 99%

Higher category theory and n-groups as gauge symmetries for quantum gravity

Nikolić,

Obrić,

Radenković

et al. 2023

J. Phys.: Conf. Ser.

View full text Add to dashboard Cite

show abstract

“…However, whenever one needs to discuss the gauge transformations off-shell, the HT subgroup simply cannot be ignored anymore. Typical situations include the Batalin-Vilkovisky formalism [1], various generalizations of gauge symmetry in the context of higher gauge theories and quantum gravity [33], and even the traditional contexts such as the Coleman-Mandula theorem [34]. The situations in which HT transformations play a significant role may be rare, but nevertheless, they tend to be important.…”

Section: The Question One Can Now Study Is What Is the Relation Betwe...mentioning

confidence: 99%

“…After discussing the Chern-Simons theory as a toy example, we move to the more important case of the 3BF theory. This theory is relevant for building models of quantum gravity; see [8,20,21,33,35]. Therefore, it is important to study its gauge symmetry and, in particular, the role of HT transformations.…”

Section: Ht Symmetry In 3bf Theorymentioning

confidence: 99%

“…Due to the antisymmetry of HT parameters, all µ blocks (below the diagonal) are determined in terms of the blocks (above the diagonal), as follows. For the first column of the parameter matrix in (33), we have:…”

Section: Explicit Ht Transformationsmentioning

confidence: 99%

“…All those possibilities are allowed, as long as the identities (38) are satisfied. The final ingredient in (33) is the expressions for the variation of the action with respect to the fields, and these are given as follows:…”

Section: Explicit Ht Transformationsmentioning

confidence: 99%

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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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Effective brane field theory with higher-form symmetry

Hidaka,

Kawana

2024

J. High Energ. Phys.

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We propose an effective field theory for branes with higher-form symmetry as a generalization of ordinary Landau theory, which is an extension of the previous work by Iqbal and McGreevy for one-dimensional objects to an effective theory for p-dimensional objects. In the case of a p-form symmetry, the fundamental field ψ[Cp] is a functional of p-dimensional closed brane Cp embedded in a spacetime. As a natural generalization of ordinary field theory, we call this theory the brane field theory. In order to construct an action that is invariant under higher-form transformation, we generalize the idea of area derivative for one-dimensional objects to higher-dimensional ones. Following this, we discuss various fundamental properties of the brane field based on the higher-form invariant action. It is shown that the classical solution exhibits the area law in the unbroken phase of U(1) p-form symmetry, while it indicates a constant behavior in the broken phase for the large volume limit of Cp. In the latter case, the low-energy effective theory is described by the p-form Maxwell theory. We also discuss brane-field theories with a discrete higher-form symmetry and show that the low-energy effective theory becomes a BF-type topological field theory, resulting in topological order. Finally, we present a concrete brane-field model that describes a superconductor from the point of view of higher-form symmetry.

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

Cited by 4 publications

References 51 publications

Higher category theory and n-groups as gauge symmetries for quantum gravity

Higher category theory and n-groups as gauge symmetries for quantum gravity

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

Effective brane field theory with higher-form symmetry

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