Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories

Fröb, Markus B.

doi:10.1007/s00220-019-03558-6

Cited by 8 publications

(21 citation statements)

References 94 publications

(265 reference statements)

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“…Since in the Breitenlohner-Maison scheme, the quantum action principle holds [25,29,35], it follows from the results of algebraic renormalization (both in flat [50,51] and curved [52][53][54] spacetimes) that it is always possible to add finite counterterms to the action to cancel spurious non-covariant terms that arise from the breaking of n-dimensional Lorentz covariance. In this way, the same criterion for the appearance of anomalies holds as in any other consistent scheme, namely that anomalies are non-trivial solutions of the Wess-Zumino consistency conditions [55], or more general, elements of a certain cohomology class of the BRST differential [50,51,56], which for diffeomorphisms is empty in four dimensions [57] (except for possible topological terms that are relevant here).…”

Section: The Modified Breitenlohner-maison Schemementioning

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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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: The Modified Breitenlohner-maison Schemementioning

confidence: 99%

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

Abdallah

Franchino-Viñas

Fröb

2021

J. High Energ. Phys.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since in the Breitenlohner-Maison scheme, the quantum action principle holds [25,29,35], it follows from the results of algebraic renormalization (both in flat [50,51] and curved [52][53][54] spacetimes) that it is always possible to add finite counterterms to the action to cancel spurious non-covariant terms that arise from the breaking of ndimensional Lorentz covariance. In this way, the same criterion for the appearance of anomalies holds as in any other consistent scheme, namely that anomalies are nontrivial solutions of the Wess-Zumino consistency conditions [55], or more general, elements of a certain cohomology class of the BRST differential [50,51,56], which for diffeomorphisms is empty in four dimensions [57] (except for possible topological terms that are relevant here).…”

Section: The Modified Breitenlohner-maison Schemementioning

confidence: 99%

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

Abdallah,

Franchino-Viñas,

Fröb

2021

Preprint

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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 parityodd contribution to the trace anomaly vanishes (for which the use of dimensiondependent 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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“…In particular, an interacting field F int A = T int A (F ) is gauge invariant if qF = 0. Furthermore, given F of ghost number 0 and fulfilling qF = 0, one may supplement it with "contact terms" to F = F + C(e F ⊗ ) such that F fulfills (75) in the sense of power series in F [56].…”

Section: F ≈ G ⇔ F − G ∈ Jāmentioning

confidence: 99%

“…We only use it in the form [Q int A , −] of the on-shell interacting BRST differential. One could equally well work with the off-shell interacting BRST differentialŝ recently constructed in [56] (which does not require compact Cauchy surfaces). For non-compact Cauchy surfaces, the construction of the cutoff functions needed, for example in Theorem 3.13 or Theorem 3.8, becomes slightly more involved, but apart from the fact that the existence of Hadamard states for non-compact Cauchy surfaces has not been proven in full generality [51], our conclusions also hold for non-compact Cauchy surfaces (with the obvious replacements of [Q int A , −] byŝ).…”

Section: Summary Of Assumptionsmentioning

confidence: 99%

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Background Independence in Gauge Theories

Tehrani

Zahn

2020

Ann. Henri Poincaré

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Classical field theory is insensitive to the split of the field into a background configuration and a dynamical perturbation. In gauge theories, the situation is complicated by the fact that a covariant (w.r.t. the background field) gauge fixing breaks this split independence of the action. Nevertheless, background independence is preserved on the observables, as defined via the BRST formalism, since the violation term is BRST exact. In quantized gauge theories, however, BRST exactness of the violation term is not sufficient to guarantee background independence, due to potential anomalies. We define background-independent observables in a geometrical formulation as flat sections of the observable algebra bundle over the manifold of background configurations, with respect to a flat connection which implements background variations. A theory is then called background independent if such a flat (Fedosov) connection exists. We analyze the obstructions to preserve background independence at the quantum level for pure Yang-Mills theory and for perturbative gravity. We find that in the former case, all potential obstructions can be removed by finite renormalization. In the latter case, as a consequence of power-counting non-renormalizability, there are infinitely many non-trivial potential obstructions to background independence. We leave open the question whether these obstructions actually occur. Contents The Free Algebra Wφ Time-Ordered Products The Interacting Algebra W int φ 2.2. Background Independence of Renormalized Scalar Field Theory 3. Pure Yang-Mills Theory 3.1. Classical Gauge Theory 3.1.1. The Basic Setting Background and Dynamical Gauge Transformations Localization of the Interaction and Split Independence 3.1.2. BV-BRST Formalism and Background Covariant Gauge Fixing Local Gauge Covariance Classical BV-BRST Cohomology The BRST Charge 3.1.3. Background-Independent Local Functionals 3.2. Perturbative Quantum Yang-Mills Theory on a BackgroundĀ 3.2.1. Ward Identities 3.2.2. Quantum BRST Charge and the Algebra of Physical Observables 3.2.3. Perturbative Agreement and the Background Dependence of the Anomaly 3.3. Background Independence 3.3.1. Well-Definedness of the Connection on the Quantum BRST Cohomology 3.3.2. Flatness of the Connection on the Quantum BRST Cohomology 3.3.3. Absence of Obstructions to Background Independence 3.3.4. Summary of Assumptions 3.3.5. Renormalized Background-Independent Interacting Fields 4. Perturbative Quantum Gravity 4.1. Background Independence as Triviality of the Relative Cauchy Evolution A Lemmata on the Anomaly References

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Anomalies in Time-Ordered Products and Applications to the BV–BRST Formulation of Quantum Gauge Theories

Cited by 8 publications

References 94 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 for Weyl fermions using the Breitenlohner-Maison scheme for $γ_*$

Background Independence in Gauge Theories

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