On gravity, torsion and the spectral action principle

Pfäffle, Frank; Stephan, Christoph A.

doi:10.1016/j.jfa.2011.11.013

Cited by 17 publications

(17 citation statements)

References 28 publications

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“…We note that the above action (20) is not valid for the more general class of torsions studied in Ref. [12]. Let us also define a traceless tensor C ab µν , as…”

Section: Fourth Order Weyl Gravitymentioning

confidence: 99%

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Linear stability of noncommutative spectral geometry

Sakellariadou

Watcharangkool

2016

Phys. Rev. D

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We consider the spectral action within the context of a 4-dimensional manifold with torsion and show that, in the vacuum case, the equations of motion reduce to Einstein's equations, securing the linear stability of the theory. To subsequently investigate the nonvacuum case, we consider the spectral action of an almost commutative torsion geometry and show that the Hamiltonian is bounded from below, a result which guarantees the linear stability of the theory.Comment: 14 page

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“…We note that the above action (20) is not valid for the more general class of torsions studied in Ref. [12]. Let us also define a traceless tensor C ab µν , as…”

Section: Fourth Order Weyl Gravitymentioning

confidence: 99%

“…Note that the torsion tensor T µνσ := 3T µνσ , whereT µνσ denotes the torsion defined in Ref. [12]. To compare S gr with S TS , we will write explicitly the torsion terms which are contained in S gr .…”

Section: Appendix A: Spin Connectionmentioning

confidence: 99%

Linear stability of noncommutative spectral geometry

Sakellariadou

Watcharangkool

2016

Phys. Rev. D

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“…If the twist bundle has a chiral asymmetry terms known from Loop Quantum Gravity ([Ro04], [Th07]) arise. The situation with purely anti-symmetric torsion has been examined before (in [HPS10], [ILV10], [PS12]), and there also are results on Dirac operators with scalar perturbations (in [SZ11]).…”

Section: Connes' Spectral Action Principle and Chiral Projectionsmentioning

confidence: 99%

Chiral Asymmetry and the Spectral Action

Pfäffle

Stephan

2012

Commun. Math. Phys.

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We consider orthogonal connections with arbitrary torsion on compact Riemannian manifolds. For the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type we compute the spectral action. In addition to the Einstein-Hilbert action and the bosonic part of the Standard Model Lagrangian we find the Holst term from Loop Quantum Gravity, a coupling of the Holst term to the scalar curvature and a prediction for the value of the Barbero-Immirzi parameter.

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“…Meanwhile, Pfäffle and Stephan considered compact Riemannian spin manifolds without boundary equipped with orthogonal connections, and investigated the induced Dirac operators in [19]. In [20], Pfäffle and Stephan considered orthogonal connections with arbitrary torsion on compact Riemannian manifolds, and for the induced Dirac operators, twisted Dirac operators and Dirac operators of Chamseddine-Connes type they computed the spectral action.…”

Section: Introductionmentioning

confidence: 99%