Weyl vs. conformal

Karananas, Georgios K.; Monin, Alexander

doi:10.1016/j.physletb.2016.04.001

Cited by 47 publications

(50 citation statements)

References 15 publications

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“…In this section we consider the free field theories of Refs. [21,23], which can be used to illustrate various aspects of the general arguments above. These theories are defined by the action…”

Section: Examplesmentioning

confidence: 99%

“…Ref. [23] showed that this theory is conformally invariant for all k and d in the sense that T = ∂ µ ∂ ν L µν in flat spacetime. However, for special values of d and k the theory cannot be improved to be Weyl invariant in curved spacetime: In general, the theory cannot be coupled to gravity in a Weyl invariant way for all values of k subject to the condition that d is even and d < 2k.…”

Section: Examplesmentioning

confidence: 99%

“…This confirms the results of Refs. [21,23] for the k = 2 theories, which are Weyl invariant unless d = 2. It also illustrates the utility of Weyl redundancy in calculations.…”

Section: Weyl Redundancymentioning

confidence: 99%

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Weyl versus conformal invariance in quantum field theory

Farnsworth

Luty

Prilepina

2017

J. High Energ. Phys.

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Abstract:We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions d ≤ 10. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible 'anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for d > 3 (d = 3). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher d with additional algebraic complexity.

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Section: Examplesmentioning

confidence: 99%

Section: Examplesmentioning

confidence: 99%

See 1 more Smart Citation

Weyl versus conformal invariance in quantum field theory

Farnsworth

Luty

Prilepina

2017

J. High Energ. Phys.

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“…The transformation properties of the fields can be obtained from the transformation of the coset representative (18). However, the structure of the commutation relations of the Galilei group (20) is not the one presented in (17). This fact results in the mixing of the U(1) gauge field with the vielbein under boosts.…”

Section: Galilei Algebramentioning

confidence: 99%

Gauging nonrelativistic field theories using the coset construction

Karananas

Monin

2016

Phys. Rev. D

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We discuss how nonrelativistic spacetime symmetries can be gauged in the context of the coset construction. We consider theories invariant under the centrally extended Galilei algebra as well as the Lifshitz one, and we investigate under what conditions they can be supplemented by scale transformations. We also clarify the role of torsion in these theories.Comment: 18 pages, no figures -- typos corrected, matches published versio

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“…In this nomenclature and related notational conventions, we have followed [30]. We should mention that some authors call this a Weyl transformation, reserving the name 'conformal transformations' for what are called 'conformal isometries' in [30] (for a discussion on the nomenclature, see [58]). This transformation alters lengths of spacetime intervals, but preserves angles.…”

Section: Introductionmentioning

confidence: 99%

Different types of torsion and their effect on the dynamics of fields

Chakrabarty

Lahiri

2018

Eur. Phys. J. Plus

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One of the formalisms that introduces torsion conveniently in gravity is the vierbein-Einstein-Palatini (VEP) formalism. The independent variables are the vierbein (tetrads) and the components of the spin connection. The latter can be eliminated in favor of the tetrads using the equations of motion in the absence of fermions; otherwise there is an effect of torsion on the dynamics of fields. We find that the conformal transformation of off-shell spin connection is not uniquely determined unless additional assumptions are made. One possibility gives rise to Nieh-Yan theory, another one to conformally invariant torsion; a one-parameter family of conformal transformations interpolates between the two. We also find that for dynamically generated torsion the spin connection does not have well defined conformal properties. In particular, it affects fermions and the non-minimally coupled conformal scalar field.

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Weyl vs. conformal

Abstract: In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way.

Cited by 47 publications

References 15 publications

Weyl versus conformal invariance in quantum field theory

Weyl versus conformal invariance in quantum field theory

Gauging nonrelativistic field theories using the coset construction

Different types of torsion and their effect on the dynamics of fields

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