Ghost and tachyon free Poincaré gauge theories: A systematic approach

Lin, Yun-Cherng; Hobson, M.; Lasenby, A.

doi:10.1103/physrevd.99.064001

Cited by 43 publications

(73 citation statements)

References 29 publications

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“…It was based on the use of spin projectors for a general two-index tensor and a three-index tensor, antisymmetric in one pair. 4 A more detailed analysis of a large number of cases including also accidental symmetries has been given recently in [30]. A broader analysis of the spectrum of a Poincaré gauge theory has been given in [31], where a class of ghost-and tachyon-free models were obtained.…”

Section: Introductionmentioning

confidence: 99%

New class of ghost- and tachyon-free metric affine gravities

2020

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We construct the spin-projection operators for a theory containing a symmetric two-index tensor and a general three-index tensor. We then use them to analyse, at linearized level, the most general action for a metric-affine theory of gravity with terms up to second order in curvature, which depends on 28 parameters. In the metric case we recover known results. In the torsion-free case, we are able to determine the most general six-parameter class of theories that are projective invariant, contain only one massless spin 2 and no spin 3, and are free of ghosts and tachyons.1 By quadratic gravity we mean theories with action containing terms linear and quadratic in the Riemann tensor.2 As an example let us mention here Weyl geometry, where φ is constructed in terms of a vector field. This theory has been revisited recently in [27].3 By accidental symmetry we mean a gauge symmetry that is present in the linearized action but not in the full action 4 This is due to the use of the vierbein formalism. The general two-index tensor is the linearized vierbein and the three-index tensor is the linearized spin connection.

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Section: Introductionmentioning

confidence: 99%

New class of ghost- and tachyon-free metric affine gravities

2020

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“…In a recent paper [1], we presented a systematic method for identifying the ghost-and-tachyon-free critical cases of parity-preserving gauge theories of gravity, and applied it to parity-preserving Poincaré gauge theory (PGT + ). The gravitational free-field Lagrangian for this theory may be written as [2] L G |b| = −λR + (r 4 + r 5 ) R AB R AB…”

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confidence: 99%

“…using the spin projection operators (SPOs)P (J P ) ij [3][4][5]. Please see Section II of [1] for a description of our notation. If any of the matrices a(J P ) is singular, then the theory possesses gauge invariances.…”

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confidence: 99%

Power-counting renormalizable, ghost-and-tachyon-free Poincaré gauge theories

Lin

Hobson²,

Lasenby

2020

Phys. Rev. D

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We present 48 further examples, in addition to the 10 identified in [1], of ghost-and-tachyon-free critical cases of parity-conserving Poincaré gauge theories of gravity (PGT + ) that are also powercounting renormalizable (PCR). This is achieved by extending the range of critical cases considered. Of the new PCR theories, 7 have 2 massless degrees of freedom (d.o.f.) in propagating modes and a massive 0 − or 2 − mode, 8 have only 2 massless d.o.f., and 33 have only massive mode(s). We also clarify the treatment of non-propagating modes in determining whether a theory is PCR. *

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“…Given that the general MAG action depends on 28 parameters, this is an extremely complicated issue. It has been partly solved in two special cases, namely when one imposes Q = 0 [15,16] or T = 0 [17]. Using F = R + ∇Φ + Φ 2 we can rewrite S(g, A) = S ′ (g, Φ) where, schematically,…”

Section: Towards Quantum Magmentioning

confidence: 99%

“…. c 16 . In fact, if we postulate δA µ ρ ν = 0, as in Yang-Mills theory, L F is even Weyl-invariant.…”

Section: Towards Quantum Magmentioning

confidence: 99%