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Categorical generalization of BF theory coupled to gravity
High Energy Physics - Theory · Submitted 6 Aug 2024
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Here, we obtain an alternative relation between BFCG and gravity, which consists of coupling general relativity and BFCG by means of the volume form constructed out of the BFCG connections.
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The abstract, sentence by sentence
We present a thorough introduction to the tools of category theory required for formulating gauge theories based on 2-connections. We provide a detailed construction of the categorical generalization of BF theory, dubbed BFCG, also known as 2BF. Similar to BF gravity, it is known that BFCG can be deformed to give general relativity. Here, we obtain an alternative relation between BFCG and gravity, which consists of coupling general relativity and BFCG by means of the volume form constructed out of the BFCG connections. The resulting theory, closely related to unimodular gravity, is a generalization of BF sequestered gravity not only in the sense that it adds new fields but also in that it allows for new choices for the volume form that is coupled to gravity. Furthermore, we show that BF sequestered gravity in the abelian case is recovered for a specific choice of the 2-group.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a thorough introduction to the tools of category theory required for formulating gauge theories based on 2-connections. | contribution 0.76 | 0.80 | 0.02 | asserted 0.98 |
| s1 | We provide a detailed construction of the categorical generalization of BF theory, dubbed BFCG, also known as 2BF. | contribution 0.98 | 0.94 | 0.08 | asserted 0.99 |
| s2 | Similar to BF gravity, it is known that BFCG can be deformed to give general relativity. | background 1.00 | 0.05 | 0.06 | asserted 0.95 |
| s3 | Here, we obtain an alternative relation between BFCG and gravity, which consists of coupling general relativity and BFCG by means of the volume form constructed out of the BFCG connections. | contribution 0.78 | 0.95 | 0.61 | asserted 1.00 |
| s4 | The resulting theory, closely related to unimodular gravity, is a generalization of BF sequestered gravity not only in the sense that it adds new fields but also in that it allows for new choices for the volume form that is coupled to gravity. | interpretation 0.46 | 0.85 | 0.37 | asserted 1.00 |
| s5 | Furthermore, we show that BF sequestered gravity in the abelian case is recovered for a specific choice of the 2-group. | result 0.98 | 0.89 | 0.12 | asserted 1.00 |
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The paper
Original abstract
We present a thorough introduction to the tools of category theory required for formulating gauge theories based on 2-connections. We provide a detailed construction of the categorical generalization of BF theory, dubbed BFCG, also known as 2BF. Similar to BF gravity, it is known that BFCG can be deformed to give general relativity. Here, we obtain an alternative relation between BFCG and gravity, which consists of coupling general relativity and BFCG by means of the volume form constructed out of the BFCG connections. The resulting theory, closely related to unimodular gravity, is a generalization of BF sequestered gravity not only in the sense that it adds new fields but also in that it allows for new choices for the volume form that is coupled to gravity. Furthermore, we show that BF sequestered gravity in the abelian case is recovered for a specific choice of the 2-group.
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What this paper does with the arXiv papers it cites
What it cites · 24 sentences without a confident label
Builds on 1 paper
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Here, we develop the fundamentals for obtaining a modified gravity theory that is coupled to several gauge fields, extending the approach presented in [ref] to higher order BF theories.
Topological Features of the Quantum Vacuum · Physical applications · 0.99
Cites as background 12 papers
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In the field of modified gravity, a new relationship between $BF$ theories and gravity has recently been proposed under the name of $BF$ sequestered gravity, in which Lagrangians for both theories are coupled such that the volume form of spacetime must coincide with the volume form constructed from one of the fields of the $BF$ theory, with this volume form acting as the potential term [ref] .
Topological Features of the Quantum Vacuum · Introduction · 0.80
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Using higher gauge theories, it is possible to generalize the $BF$ theory, leading to formulations of topological field theories [ref] , for instance, $BFCG$ (also known as $2BF$) for 2-categories and $3BF$ for 3-categories (see [ref] ).
Topological Higher Gauge Theory - from BF to BFCG theory · Introduction · 0.89
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Using higher gauge theories, it is possible to generalize the $BF$ theory, leading to formulations of topological field theories [ref] , for instance, $BFCG$ (also known as $2BF$) for 2-categories and $3BF$ for 3-categories (see [ref] ).
Hamiltonian analysis of the BFCG theory for a strict Lie 2-group · Introduction · 0.89
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