Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”

Kreimer, Dirk; Mielke, Eckehard W.

doi:10.1103/physrevd.63.048501

Cited by 60 publications

(42 citation statements)

References 30 publications

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“…The addition of the Pontrjagin term with respect to the Riemannian curvature R {} αβ and the axial torsion one-form A := * (ϑ α ∧ T α ) is motivated by the the axial anomaly d j 5 2 in the coupling to Dirac fields ψ, cf. [22].…”

Section: Self-dual Sky Gravitymentioning

confidence: 95%

Duality in Yang’s theory of gravity

Mielke

Maggiolo

2005

Gen Relativ Gravit

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The historical route and the current status of a curvature-squared model of gravity, in the affine form proposed by Yang, is briefly reviewed. Due to its inherent scale invariance, it enjoys some advantage for quantization, similarly as internal Yang-Mills fields. However, the exact vacuum solutions with double duality properties exhibit a 'vacuum degeneracy'. By modifying the duality via a scale breaking term, we demonstrate that only the Einstein equations with induced cosmological constant emerge for the classical background, even when coupled to matter sources.

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Section: Self-dual Sky Gravitymentioning

confidence: 95%

Duality in Yang’s theory of gravity

Mielke

Maggiolo

2005

Gen Relativ Gravit

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“…There is a controversy whether the second term in (4.1), which is by itself a topological invariant, should contribute to the chiral anomaly or not. See [42] and [43] for details. The AdS/CFT correspondence offers a rich ground to test the dependence of the chiral anomaly on torsion.…”

Section: Discussionmentioning

confidence: 99%

Holographic currents in first order Gravity and finite Fefferman-Graham expansions

Bañados¹,

Mišković²,

Theisen³

2006

J. High Energy Phys.

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Abstract:We study the holographic currents associated to Chern-Simons theories. We start with an example in three dimensions and find the holographic representations of vector and chiral currents reproducing the correct expression for the chiral anomaly. In five dimensions, Chern-Simons theory for AdS group describes first order gravity and we show that there exists a gauge fixing leading to a finite Fefferman-Graham expansion. We derive the corresponding holographic currents, namely, the stress tensor and spin current which couple to the metric and torsional degrees of freedom at the boundary, respectively. We obtain the correct Ward identities for these currents by looking at the bulk constraint equations.

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“…The latter contains, amongst others, a term proportional to the Riemannian curvature scalar R {} := * (R {}αβ ∧ η β α ) and the axial torsion piece dA ∧ dA of the axial anomaly [32,43] with a relative factor 9. Up to normalizations, the four-forms (26) and (28) are known as Nieh-Yan [52] and gravitational Pontrjagin term, respectively.…”

Section: Appendix A: Riemann-cartan Geometry In Clifford Algebra-valumentioning

confidence: 99%

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)]

Mielke¹

2008

Phys. Rev. D

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INTRODUCTIONOn the macroscopical level, Einstein's general relativity has passed every test "with flying colors", see Will [67] for a recent review. However, Einstein's theory sofar has resisted any attempt of quantization, e.g. it is known to be perturbatively nonrenormalizable, partially due to its dimensional coupling constant 2 . String theory or brane scenarios with extra dimensions have been proposed as a rescue, some of which are implying, however, deviations of standard gravity in the sub-millimeter range. Recent torsion balance experiments [28] have probed the inverse square law and found no deviation even below the hypothetical dark energy (DE) scale of λ DE = (hc/ρ DE ) 1/4 ≃ 85 µm. Thus this 'window' of possibly new gravitational physics seems also to be closing.In 1974 Yang proposed an affine gauge theory gravity [70] which, due to its scale invariance, can be regarded as a rather promising fundamental theory of (quantum) gravity in the high-energy limit [25], without invoking extra dimensions or supersymmetry, cf. Ref. [30]. An additional duality constraint on the curvature could be extremely important for the path integral approach to quantum gravity. Then instanton type configurations [22] near the classical ones, i.e. Einstein spaces, are more probable then the 'spurious' Thomson spaces, as one would expect naively. For the modified duality with a breaking of scale invariance, the transition amplitude peaks at classical Einstein spaces only. Alternatively, in a four-dimensional Yang-Mills theory gauging the de Sitter group [37,54], scale invariance gets spontaneously broken by a pseudo-Goldstone type 'radius vector' [62], odd under CP, in order to recover the Hilbert-Einstein action plus the Euler term.From the work of Stelle [59] we know that the curvature squared gravity in Riemannian spacetime is perturbatively renormalizable but unfortunately plagued with physical ghost, i.e. negative residues in the graviton propagator [36]. This finding has diminished 1 E-mail: ekke@xanum.uam.mx 2 It has to be kept in mind that Newton's gravitational constant G is one of the less precise known constants of physics. In order to improve this situation, there are plans [1] to measure the gravitational attraction of two bodies in a spaceship (Project SEE), where the larger body will function as a shepherd for the movement of the test mass, similarly as in the rings of Saturn. Amongst others, an accuracy of 3.3 × 10 −7 in the determination of G should be feasible. the initial interest [19,20] in such models.Much more promising and elegant is to start from a purely topological classical action, proportional to the gravitational Pointrjagin (or Euler) invariant and then quantize this model by nilpotent Becchi-Rouet-Stora-Tyutin (BRST) transformations generated by s. Such a topological action is not only completely metric-free, but moreover conformally invariant [69,34] and can provide a consistent Topological Quantum Field Theory (TQFT) as shown by Witten [68,9]. Lateron, it was realized by Baulieu and Singer [6]...

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Comment on “Topological invariants, instantons, and the chiral anomaly on spaces with torsion”

Cited by 60 publications

References 30 publications

Duality in Yang’s theory of gravity

Duality in Yang’s theory of gravity

Holographic currents in first order Gravity and finite Fefferman-Graham expansions

Publisher’s Note: Einsteinian gravity from BRST quantization of a topological action [Phys. Rev. D77, 084020 (2008)]

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