Induced gravity for nonzero torsion

Grensing, Gerhard

doi:10.1016/0370-2693(86)90367-9

Cited by 9 publications

(11 citation statements)

References 15 publications

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“…In [ILV10] it has been noted that some terms given in [HPS10] vanish. Similar results have been found before (compare [Go80], [Ob83], [Gr86]). The calculation given below is elementary, it takes place essentially in the tangent bundle and should therefore be easily accessible.…”

Section: Commutative Geometries and The Spectral Action Principlesupporting

confidence: 92%

On gravity, torsion and the spectral action principle

Pfäffle

Stephan

2012

Journal of Functional Analysis

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Section: Commutative Geometries and The Spectral Action Principlesupporting

confidence: 92%

On gravity, torsion and the spectral action principle

Pfäffle

Stephan

2012

Journal of Functional Analysis

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“…So, in agreement with [5,11,40,41] we find no Nieh-Yan term in the anomaly. But at this stage we have not discussed the possibility that the torsion is not adiabatically connected to the torsion-free case.…”

Section: Chiral Anomaly In Quantum Field Theorysupporting

confidence: 86%

“…Quantum anomalies both in the Riemannian and in the Riemann-Cartan spacetimes were calculated previously in several papers using different methods, see e.g. [5,11,40,41,7].…”

Section: Introductionmentioning

confidence: 99%

Chiral Anomaly in Contorted Spacetimes

Mielke¹,

Kreimer²

1999

General Relativity and Gravitation

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The Dirac equation in Riemann-Cartan spacetimes with torsion is reconsidered. As is well-known, only the axial covector torsion $A$, a one-form, couples to massive Dirac fields. Using diagrammatic techniques, we show that besides the familiar Riemannian term only the Pontrjagin type four-form $dA\wedge dA$ does arise additionally in the chiral anomaly, but not the Nieh-Yan term $d ^* A$, as has been claimed recently. Implications for cosmic strings in Einstein-Cartan theory as well as for Ashtekar's canonical approach to quantum gravity are discussed.Comment: 17 pages, REVTE

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“…The spectral action associated to a manifold endowed with a connection with torsion has been computed recently in [23], though technical tools were ready long ago [20,21,34]. The extension by torsion [23] of the almost commutative spectral triple of the standard model in particle physics [9] demonstrated that torsion becomes coupled to the Higgs field and, therefore is possibly observable.…”

Section: Introductionmentioning

confidence: 99%

Spectral Action for Torsion with and without Boundaries

Iochum

Lévy

Vassilevich

2012

Commun. Math. Phys.

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We derive a commutative spectral triple and study the spectral action for a rather general geometric setting which includes the (skew-symmetric) torsion and the chiral bag conditions on the boundary. The spectral action splits into bulk and boundary parts. In the bulk, we clarify certain issues of the previous calculations, show that many terms in fact cancel out, and demonstrate that this cancellation is a result of the chiral symmetry of spectral action. On the boundary, we calculate several leading terms in the expansion of spectral action in four dimensions for vanishing chiral parameter θ of the boundary conditions, and show that θ = 0 is a critical point of the action in any dimension and at all orders of the expansion.

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Induced gravity for nonzero torsion

Cited by 9 publications

References 15 publications

On gravity, torsion and the spectral action principle

On gravity, torsion and the spectral action principle

Chiral Anomaly in Contorted Spacetimes

Spectral Action for Torsion with and without Boundaries

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