Axial gravity and anomalies of fermions

Bastianelli, Fiorenzo; Broccoli, Matteo

doi:10.1140/epjc/s10052-020-7782-4

Cited by 23 publications

(24 citation statements)

References 32 publications

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“…Employing the Breitenlohner-Maison scheme [25] for the treatment of the chiral matrix γ * , we did not find any parity-odd contributions to the expectation value. Therefore, also the trace anomaly does not contain any parity-odd term proportional to the Pontryagin density, and the result for the trace anomaly is half the one of a Dirac fermion, as also confirmed using other methods [7][8][9]. This result reaffirms the validity of the equivalence principle for the coupling of matter to gravity in the present case, since there is no difference between left-or right-handed fermions.…”

Section: Discussionsupporting

confidence: 87%

“…These results were derived in dimensional regularization, both using a standard perturbative computation around Minkowski spacetime using Feynman diagrams and introducing an "metric-axial-tensor gravity" approach similar to JHEP03(2021)271 the axial vector potential in gauge theory. However, with strictly four-dimensional regularization methods such as Pauli-Villars regularization [7,8] employed by Bastianelli et al, or Hadamard subtraction used by Zahn and the last author [9], CP-odd terms in the trace anomaly do not arise at all. In between, this has given rise to more general discussions involving gauge anomalies [10,11] and general CP-violating theories [12,13].…”

Section: Introductionmentioning

confidence: 99%

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Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

Abdallah

Franchino-Viñas

Fröb

2021

J. High Energ. Phys.

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We revisit the computation of the trace anomaly for Weyl fermions using dimensional regularization. For a consistent treatment of the chiral gamma matrix γ* in dimensional regularization, we work in n dimensions from the very beginning and use the Breitenlohner-Maison scheme to define γ*. We show that the parity-odd contribution to the trace anomaly vanishes (for which the use of dimension-dependent identities is crucial), and that the parity-even contribution is half the one of a Dirac fermion. To arrive at this result, we compute the full renormalized expectation value of the fermion stress tensor to second order in perturbations around Minkowski spacetime, and also show that it is conserved.

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Section: Discussionsupporting

confidence: 87%

Section: Introductionmentioning

confidence: 99%

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

Abdallah

Franchino-Viñas

Fröb

2021

J. High Energ. Phys.

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“…Since the coefficient of the parity-odd Pontryagin density vanishes, no unitarity problem arises in the quantum theory. The result for the trace anomaly is half of the result for a Dirac fermion, in agreement with [27][28][29], but contrary to [11,30]. It thus seems that the prescription for γ * that was employed in the latter works is not consistent.…”

Section: Discussionsupporting

confidence: 47%

“…Trace anomaly of Weyl fermions S. Abdallah and S. A. Franchino-Viñas reduced to a Fujikawa-like calculation [27]. Afterwards, they have extended their Pauli-Villars regularization to consider a metric-axial-tensor background (i.e., the idea developed by Bonora et al [13]), obtaining once more a vanishing contribution for the parity-odd term [28]. Their result also includes the fact that the (parity-even) conformal anomaly in the Weyl case is half the one for a Dirac fermion.…”

Section: Pos(eps-hep2021)723mentioning

confidence: 99%

Trace anomaly of Weyl fermions in the Breitenlohner--Maison scheme for $\gamma_*$

Abdallah¹,

Franchino-Viñas²,

Fröb³

2022

Proceedings of the European Physical Society Conference on High Energy Physics — PoS(EPS-HEP2021)

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We revisit the conformal anomaly for a Weyl fermion in four dimensions that has generated some debate recently. We employ a perturbative expansion for the metric around Minkowski space, dimensional regularization and a Breitenlohner-Maison prescription for the chiral γ matrix. We obtain a vanishing odd-parity contribution for Weyl fermions in four dimensions, while the evenparity contribution is exactly half the one for a Dirac fermion.

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“…Obviously, studies of 1-particle irreducible effective actions in gravitational backgrounds are common in the literature (see for instance [21][22][23][24]), for instance in a E/m expansion, in the presence of massive intermediate states. More recent investigations of conformal correlators both for chiral and conformal anomalies are those of [25][26][27]. For our goals, we will review the origin of the nonlocal Riegert action pedagogically, detailing the variational solution of the anomaly constraint by integration in field space, which takes to such expression.…”

Section: Introductionmentioning

confidence: 99%

On some hypergeometric solutions of the conformal Ward identities of scalar 4-point functions in momentum space

Corianò

Maglio

2019

J. High Energ. Phys.

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We discuss specific hypergeometric solutions of the conformal Ward identities (CWI's) of scalar 4-point functions of primary fields in momentum space, in d spacetime dimensions. We determine such solutions using various dual conformal ansätze (DCA's). We start from a generic dual conformal correlator, and require it to be conformally covariant in coordinate space. The two requirements constrain such solutions to take a unique hypergeometric form. They describe correlators which are at the same time conformal and dual conformal in any dimension. These specific ansätze also show the existence of a link between 3-and 4-point functions of a CFT for such class of exact solutions, similarly to what found for planar ladder diagrams. We show that in d = 4 only the box diagram and its melonic variants, in free field theory, satisfies such conditions, the remaining solutions being nonperturbative. We then turn to the analysis of some approximate high energy fixed angle solutions of the CWI's which also in this case take the form of generalized hypergeometric functions. We show that they describe the behaviour of the 4-point functions at large energy and momentum transfers, with a fixed −t/s. The equations, in this case, are solved by linear combinations of Lauricella functions of 3 variables and can be rewritten as generalized 4K integrals. In both cases the CWI's alone are sufficient to identify such solutions and their special connection with generalized hypergeometric systems of equations.Using the definitons above, each equation can be characterized in terms of the set of operators

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Axial gravity and anomalies of fermions

Cited by 23 publications

References 32 publications

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

Trace anomaly for Weyl fermions using the Breitenlohner-Maison scheme for γ*

Trace anomaly of Weyl fermions in the Breitenlohner--Maison scheme for $\gamma_*$

On some hypergeometric solutions of the conformal Ward identities of scalar 4-point functions in momentum space

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