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

Helayël-Neto, J. A.; Penna-Firme, André; Shapiro, Ilya L.

doi:10.1016/s0370-2693(00)00342-7

Cited by 38 publications

(63 citation statements)

References 27 publications

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“…The on-shell equivalence can be also verified using the equations of motion [102]. It is easy to check, by direct inspection, that even off-shell, the theory with torsion (2.43), satisfying the relation (2.47), may be conformally invariant whenever we define the transformation law for the torsion trace according to (2.52): and also postulate that the other pieces of torsion: S µ and q α · βγ , do not transform.…”

Section: Conformal Properties Of Torsionmentioning

confidence: 92%

“…Conformal symmetry with torsion has been studied in many papers (see, for example, [141,36,102] and references therein). Here, we shall summarize the results obtained in [36,102].…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

“…iii) Compensating conformal symmetry [141,102]. This is the most interesting and complicated version of the conformal transformation.…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

“…The effect of changing conformal value of ξ due to the nontrivial transformation of torsion has been discussed in [149] and [102] (see also further references there).…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

“…In the book [34] the quantum theory on curved background with torsion has been also considered. We shall rely on the formalism developed in [36,166,37,4,33,32,34,102], and consider some additional applications 1 .…”

Section: An Example Of the Possible Effect Of Classical Torsionmentioning

confidence: 99%

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Physical aspects of the space–time torsion

2002

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Abstract. We review many quantum aspects of torsion theory and discuss the possibility of the space-time torsion to exist and to be detected. The paper starts, in Chapter 2, with a pedagogical introduction to the classical gravity with torsion, that includes also interaction of torsion with matter fields. Special attention is paid to the conformal properties of the theory. In Chapter 3, the renormalization of quantum theory of matter fields and related topics, like renormalization group, effective potential and anomalies, are considered. Chapter 4 is devoted to the action of spinning and spinless particles in a space-time with torsion, and to the discussion of possible physical effects generated by the background torsion. In particular, we review the upper bounds for the magnitude of the background torsion which are known from the literature. In Chapter 5, the comprehensive study of the possibility of a theory for the propagating completely antisymmetric torsion field is presented. It is supposed that the propagating field should be quantized, and that its quantum effects must be described by, at least, some effective low-energy quantum field theory. We show, that the propagating torsion may be consistent with the principles of quantum theory only in the case when the torsion mass is much greater than the mass of the heaviest fermion coupled to torsion. Then, universality of the fermion-torsion interaction implies that torsion itself has a huge mass, and can not be observed in realistic experiments. Thus, the theory of quantum matter fields on the classical torsion background can be formulated in a consistent way, while the theory of dynamical torsion meets serious obstacles. In Chapter 6, we briefly discuss the string-induced torsion and the possibility to induce torsion action and torsion itself through the quantum effects of matter fields.

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Section: Conformal Properties Of Torsionmentioning

confidence: 92%

“…Conformal symmetry with torsion has been studied in many papers (see, for example, [141,36,102] and references therein). Here, we shall summarize the results obtained in [36,102].…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

“…iii) Compensating conformal symmetry [141,102]. This is the most interesting and complicated version of the conformal transformation.…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

“…The effect of changing conformal value of ξ due to the nontrivial transformation of torsion has been discussed in [149] and [102] (see also further references there).…”

Section: Conformal Properties Of Torsionmentioning

confidence: 99%

Section: An Example Of the Possible Effect Of Classical Torsionmentioning

confidence: 99%

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Physical aspects of the space–time torsion

2002

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Conformal transformations in metric‐affine gravity and ghosts

2012

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Conformal transformations play a widespread role in gravity theories in regard to their cosmological and other implications. In the pure metric theory of gravity, conformal transformations change the frame to a new one wherein one obtains a conformal-invariant scalar-tensor theory such that the scalar field, deriving from the conformal factor, is a ghost. In this work, conformal transformations and ghosts will be analyzed in the framework of the metric-affine theory of gravity. Within this framework, metric and connection are independent variables, and, hence, transform independently under conformal transformations. It will be shown that, if affine connection is invariant under conformal transformations, then the scalar field of concern is a non-ghost, non-dynamical field. It is an auxiliary field at the classical level, and might develop a kinetic term at the quantum level. Alternatively, if connection transforms additively with a structure similar to yet more general than that of the LeviCivita connection, the resulting action describes the gravitational dynamics correctly, and, more importantly, the scalar field becomes a dynamical non-ghost field. The equations of motion, for generic geometrical and matter-sector variables, do not reduce connection to the Levi-Civita connection, and, hence, independence of connection from metric is maintained. Therefore, metric-affine gravity provides an arena in which ghosts arising from the conformal factor are avoided thanks to the independence of connection from the metric.

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Special Sections

Shapiro¹

2019

Undergraduate Lecture Notes in Physics

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

Cited by 38 publications

References 27 publications

Physical aspects of the space–time torsion

Physical aspects of the space–time torsion

Conformal transformations in metric‐affine gravity and ghosts

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