Self-dual 2-forms and gravity

Capovilla, Riccardo; Dell, John; Jacobson, Ted; Mason, Lionel

doi:10.1088/0264-9381/8/1/009

Cited by 268 publications

(533 citation statements)

References 25 publications

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“…while from dT = 0 one obtains 6) because also the twist-deformed exterior product is associative [7]. Thus, we find the simple but nontrivial property…”

Section: S = Tr Irmentioning

confidence: 72%

“…(11.2) is found to have, in the neighborhood of θ αβ = 0, the asymptotic expansion 6) where the term independent of θ αβ on the right-hand side of (11.6) gives a vanishing con- …”

Section: Equations For the Tetrad And Their Solutionmentioning

confidence: 99%

“…10.1 of Ref. [2]) and supergravity [3], as well as in gravitational instanton theory [4] and in modern approaches to the Hamiltonian formulation of general relativity [5,6]. Within this framework, one assumes that a set of local Lorentz frames exist, whose global existence is ensured if the classical spacetime manifold is parallelizable.…”

Section: Introductionmentioning

confidence: 99%

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Self-dual road to noncommutative gravity with twist: A new analysis

2014

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The field equations of noncommutative gravity can be obtained by replacing all exterior products by twist-deformed exterior products in the action functional of general relativity, and are here studied by requiring that the torsion 2-form should vanish, and that the Lorentz-Lie-algebravalued part of the full connection 1-form should be self-dual. Other two conditions, expressing self-duality of a pair 2-forms occurring in the full curvature 2-form, are also imposed. This leads to a systematic solution strategy, here displayed for the first time, where all parts of the connection 1-form are first evaluated, hence the full curvature 2-form, and eventually all parts of the tetrad 1-form, when expanded on the basis of γ-matrices. By assuming asymptotic expansions which hold up to first order in the noncommutativity matrix in the neighbourhood of the vanishing value for noncommutativity, we find a family of self-dual solutions of the field equations. This is generated by solving first a inhomogeneous wave equation on 1-forms in a classical curved spacetime (which is itself self-dual and solves the vacuum Einstein equations), subject to the Lorenz gauge condition.In particular, when the classical undeformed geometry is Kasner spacetime, the above scheme is fully computable out of solutions of the scalar wave equation in such a Kasner model.

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“…while from dT = 0 one obtains 6) because also the twist-deformed exterior product is associative [7]. Thus, we find the simple but nontrivial property…”

Section: S = Tr Irmentioning

confidence: 72%

“…(11.2) is found to have, in the neighborhood of θ αβ = 0, the asymptotic expansion 6) where the term independent of θ αβ on the right-hand side of (11.6) gives a vanishing con- …”

Section: Equations For the Tetrad And Their Solutionmentioning

confidence: 99%

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Self-dual road to noncommutative gravity with twist: A new analysis

2014

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“…In the case of general relativity, it has been shown in Ref. [2] that the action for gravity in terms of Ashtekar variables [12,13,14,15,16] is gauge-invariant up to a term proportional to the Hamiltonian constraint under the gauge symmetry generated by their first class constraints. This suggests that if one starts from the action for gravity in terms of Arnowitt-Deser-Misner (ADM) variables in its triad version [17] and apply Eq.…”

Section: Discussionmentioning

confidence: 99%

Linear constraints from generally covariant systems with quadratic constraints

Montesinos

Vergara

2002

Phys. Rev. D

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How to make compatible both boundary and gauge conditions for generally covariant theories using the gauge symmetry generated by first class constraints is studied. This approach employs finite gauge transformations in contrast with previous works which use infinitesimal ones. Two kinds of variational principles are taken into account; the first one features non-gauge-invariant actions whereas the second includes fully gauge-invariant actions. Furthermore, it is shown that it is possible to rewrite fully gauge-invariant actions featuring first class constraints quadratic in the momenta into first class constraints linear in the momenta (and homogeneous in some cases) due to the full gauge invariance of their actions. This shows that the gauge symmetry present in generally covariant theories having first class constraints quadratic in the momenta is not of a different kind with respect to the one of theories with first class constraints linear in the momenta if fully gaugeinvariant actions are taken into account for the former theories. These ideas are implemented for the parametrized relativistic free particle, parametrized harmonic oscillator, and the SL(2, R) model.

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“…There appear two kinds of supersymmetry (SUSY) transformations, namely, right-and left-handed SUSY transformations. After that, the first-order formulation of N = 1 chiral SUGRA was made using the method of the two-form gravity [4,5]. However, in the two-form SUGRA, the SUSY transformation parameters are constrained and the problem of the off-shell closure of SUSY algebra is still open.…”

mentioning

confidence: 99%

Minimal off-shell version ofN=1chiral supergravity

Tsuda

Shirafuji

1998

Phys. Rev. D

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We construct the minimal off-shell formulation of N = 1 chiral supergravity (SUGRA) introducing a complex antisymmetric tensor field B µν and a complex axial-vector field A µ as auxiliary fields. The resulting algebra of the right-and left-handed supersymmetry (SUSY) transformations closes off shell and generates chiral gauge transforamtions and vector gauge transformations in addition to the transformations which appear in the case without auxiliary fields.

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Self-dual 2-forms and gravity

Cited by 268 publications

References 25 publications

Self-dual road to noncommutative gravity with twist: A new analysis

Self-dual road to noncommutative gravity with twist: A new analysis

Linear constraints from generally covariant systems with quadratic constraints

Minimal off-shell version ofN=1chiral supergravity

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