Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion

A. Penna-Firme; I. L. Shapiro; J.A. Helayel-Neto

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Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion

J.A. Helayel-Neto, A. Penna-Firme, I. L. Shapiro

General Relativity and Quantum Cosmology · Submitted 26 Jul 1999

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The authors' main claim It is shown that, for some special choice of the action, torsion acts as a compensating field and the full theory is conformally equivalent to General Relativity on classical level.

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arXiv IDgr-qc/9907081 (version 2)

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CitationA. Penna-Firme, I. L. Shapiro, J.A. Helayel-Neto. "Conformal symmetry, anomaly and effective action for metric-scalar gravity with torsion." arXiv:gr-qc/9907081 (1999). https://pith.science/paper/EHAK3CKD

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We consider some aspects of conformal symmetry in a metric-scalar-torsion system. It is shown that, for some special choice of the action, torsion acts as a compensating field and the full theory is conformally equivalent to General Relativity on classical level. Due to the introduction of torsion, this equivalence can be provided for the positively-defined gravitational and scalar actions. One-loop divergences arising from the scalar loop are calculated and both the consequent anomaly and the anomaly-induced effective action are derived.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We consider some aspects of conformal symmetry in a metric-scalar-torsion system.	contribution 0.57	0.76	0.05	unclear 0.52
s1	It is shown that, for some special choice of the action, torsion acts as a compensating field and the full theory is conformally equivalent to General Relativity on classical level.	result 0.99	0.88	0.51	asserted 1.00
s2	Due to the introduction of torsion, this equivalence can be provided for the positively-defined gravitational and scalar actions.	result 0.63	0.70	0.16	asserted 0.92
s3	One-loop divergences arising from the scalar loop are calculated and both the consequent anomaly and the anomaly-induced effective action are derived.	result 0.79	0.95	0.27	asserted 1.00

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Original abstract

We consider some aspects of conformal symmetry in a metric-scalar-torsion system. It is shown that, for some special choice of the action, torsion acts as a compensating field and the full theory is conformally equivalent to General Relativity on classical level. Due to the introduction of torsion, this equivalence can be provided for the positively-defined gravitational and scalar actions. One-loop divergences arising from the scalar loop are calculated and both the consequent anomaly and the anomaly-induced effective action are derived.

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7 arXiv papers cite this in 8 sentences

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For example, the form of the anomaly in the Riemann-Cartan case has been discussed by several authors [ref] , while in the more general case of MAG, particularly regarding the effects of nonmetricity, it has not yet been thoroughly explored, to the best of our knowledge.

Trace Anomaly in Metric-Affine gravity · Introduction · 0.82
It is noteworthy to mention that Ref. [ref] discusses also a third type of conformal transformation, initially introduced in Ref. [ref] and referred to as “compensating” conformal symmetry.

Weyl cohomology and the conformal anomaly in the presence of torsion · Introduction · 0.95
See e.g. [ref] for interesting discussions on conformal transformations involving torsion.] given by g_μν→e^2Ωg_μν, T_μ→T_μ+3∂_μΩwith $Ω$ and arbitrary function, we have that the Ricci scalar transforms as $R→e^-2ΩR$.

Revisiting the Stability of Quadratic Poincar\'e Gauge Gravity · $R^2$ theories · 0.87

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