Weyl cocycles

Bonora, L.; Pasti, P.; Bregola, M.

doi:10.1088/0264-9381/3/4/018

Cited by 180 publications

(304 citation statements)

References 17 publications

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“…In six dimensions this special invariant matches with a particular combination pointed out by Bonora, Pasti and Bregola in ref. [16], and in higher even dimensions agrees with the Henningson-Skenderis construction [17]. Quantum field theory is the most powerful algorithm to study these mathematical properties.…”

Section: The Use Of Non-unitary Theoriessupporting

confidence: 58%

A universal flow invariant in quantum field theory

Anselmi¹

2001

Class. Quantum Grav.

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A flow invariant is a quantity depending only on the UV and IR conformal fixed points and not on the flow connecting them. Typically, its value is related to the central charges a and c. In classically-conformal field theories scale invariance is broken by quantum effects and the flow invariant a UV − a IR is measured by the area of the graph of the beta function between the fixed points. There exists a theoretical explanation of this non-trivial fact. On the other hand, when scale invariance is broken at the classical level, it is empirically known that the flow invariant equals c UV − c IR in massive free-field theories, but a theoretical argument explaining why it is so is still missing. A number of related open questions are answered here. A general formula of the flow invariant is found, which holds also when the stress tensor has improvement terms. The conditions under which the flow invariant equals c UV − c IR are identified. Several non-unitary theories are used as a laboratory, but the conclusions are general and an application to the Standard Model is addressed. The analysis of the results suggests some new minimum principles, which might point towards a new understanding of quantum field theory.

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Section: The Use Of Non-unitary Theoriessupporting

confidence: 58%

A universal flow invariant in quantum field theory

Anselmi¹

2001

Class. Quantum Grav.

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“…In two space-time dimensions for example, only one anomaly exists in the relative cohomology which is proportional to: 10) and there are no coboundary terms. In four space-time dimensions [29][30][31], the possible scalar expressions of dimension 4 are:…”

Section: Jhep02(2015)078mentioning

confidence: 99%

Lifshitz scale anomalies

Arav

Chapman

2015

J. High Energ. Phys.

106

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We analyse scale anomalies in Lifshitz field theories, formulated as the relative cohomology of the scaling operator with respect to foliation preserving diffeomorphisms. We construct a detailed framework that enables us to calculate the anomalies for any number of spatial dimensions, and for any value of the dynamical exponent. We derive selection rules, and establish the anomaly structure in diverse universal sectors. We present the complete cohomologies for various examples in one, two and three space dimensions for several values of the dynamical exponent. Our calculations indicate that all the Lifshitz scale anomalies are trivial descents, called B-type in the terminology of conformal anomalies. However, not all the trivial descents are cohomologically non-trivial. We compare the conformal anomalies to Lifshitz scale anomalies with a dynamical exponent equal to one.

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“…The general expression of 6d trace anomalies can be obtained from a cohomological analysis [17,16] and is of the form…”

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confidence: 99%

Simplified method for trace anomaly calculations ind<~6

Bastianelli

Dass

2001

Phys. Rev. D

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We discuss a simplified method for computing trace anomalies in dimensions d ≤ 6. It is known that in the quantum mechanical approach trace anomalies in d dimensions are given by a ( d 2 + 1)-loop computation in an auxiliary 1d sigma model with arbitrary geometry. We show how one can obtain the same information using a simpler d 2 -loop calculation on an arbitrary geometry supplemented by a ( d 2 + 1)-loop calculation on the simplified geometry of a maximally symmetric space.

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Weyl cocycles

Cited by 180 publications

References 17 publications

A universal flow invariant in quantum field theory

A universal flow invariant in quantum field theory

Lifshitz scale anomalies

Simplified method for trace anomaly calculations ind<~6

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