Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Herfray, Yannick

doi:10.1063/1.5012268

Cited by 9 publications

(7 citation statements)

References 29 publications

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“…This turns out to be true, there is a direct link between the twistor space description of instantons and (39). Details of this relation have been worked out in [44], where we refer the reader for more details.…”

Section: Twistor Space Descriptionmentioning

confidence: 82%

Self-dual gravity

Krasnov

2017

Class. Quantum Grav.

101

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Self-dual gravity is a diffeomorphism invariant theory in four dimensions that describes two propagating polarisations of the graviton and has a negative mass dimension coupling constant. Nevertheless, this theory is not only renormalisable but quantum finite, as we explain. We also collect various facts about self-dual gravity that are scattered across the literature.1 Another not very physical feature of self-dual gravity is that many of its scattering amplitudes vanish, see below.

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Section: Twistor Space Descriptionmentioning

confidence: 82%

Self-dual gravity

Krasnov

2017

Class. Quantum Grav.

101

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“…where ε i jk is the totally anti-symmetric Levi-Civita tensor, and δ i j is the Kronecker delta. This relates to the fact that the complexified Lie algebra of SO(3, 1) has the decomposition so(3, 1) C = so(3, C) ⊕ so(3, C) [6]. The new connection is locally an so(3, C)-valued 1-form A on M whose components are…”

Section: Spin Current In Bf Theorymentioning

confidence: 99%

“…Furthermore, the condition DB i = 0 is necessary when the connection A i is flat, by that the 2-form B i belongs to the twisted de Rham cohomology classes H 2 DR (M, so(3, C) P ), and this is necessary for getting a topological theory. One can solve that problem by adding new terms to the BF action (6) with which there are many possibilities for controlling Equation (10) for J µi = 0 with choosing DB i = 0. Only some simple possibilities are chosen below in order to get simple results.…”

Section: Definitionmentioning

confidence: 99%

Spin Current in BF Theory

Almatwi

2021

Physics

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In this paper, a current that is called spin current and corresponds to the variation of the matter action in BF theory with respect to the spin connection A which takes values in Lie algebra so(3,C), in self-dual formalism is introduced. For keeping the 2-form Bi constraint (covariant derivation) DBi=0 satisfied, it is suggested adding a new term to the BF Lagrangian using a new field ψi, which can be used for calculating the spin current. The equations of motion are derived and the solutions are dicussed. It is shown that the solutions of the equations do not require a specific metric on the 4-manifold M, and one just needs to know the symmetry of the system and the information about the spin current. Finally, the solutions for spherically and cylindrically symmetric systems are found.

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“…That self-dual projection relates to the fact that the complexified Lie algebra of SO (3,1) has the decomposition so(3, 1) C = so(3, C) ⊕ so(3, C) [6]. The new connection is locally an so(3, C)-valued 1-form A on M whose components are…”

Section: Spin Current In Bf Theorymentioning

confidence: 99%

Spin current in BF theory

Matwi

2021

Preprint

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In this paper, we introduce a current which we call spin current corresponding to the variation of the matter action in BF theory with respect to the spin connection A which takes 1 values in Lie algebra so(3, C) in self-dual formalism. For keeping the constraint DB i = 0 satisfied, we suggest adding a new term to the BF Lagrangian using a new field ψ i which can be used for calculating the spin current. We derive the equations of motion and discuss the solutions. We will see that the solutions of that equations do not require a specific metric on the manifold M, we just need to know the symmetry of the system and the information about the spin current. Finally we find the solutions in a spherical and cylindrical symmetric systems.

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Pure connection formulation, twistors, and the chase for a twistor action for general relativity

Cited by 9 publications

References 29 publications

Self-dual gravity

Self-dual gravity

Spin Current in BF Theory

Spin current in BF theory

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