Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups

Karakhanyan, D.; Manvelyan, Ruben; Mkrtchyan, R. L.

doi:10.1142/s021773239600045x

Cited by 29 publications

(37 citation statements)

References 6 publications

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“…The number of independent A B rises rapidly with dimension; for example there are [4] three varieties at D=6: two independent index traces of √ −g C 3 and a third of the schematic form √ −g trC(✷ + R)C. An effective D=4 action that reflects the required logarithmic behavior was already introduced in [3] at lowest, cubic, order in an expansion about flat space, h µν ≡ g µν − η µν :…”

Section: Type Bmentioning

confidence: 99%

Closed form effective conformal anomaly actions in D≥4

Deser

2000

Physics Letters B

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I present, in any D≥4, closed-form type B conformal anomaly effective actions incorporating the logarithmic scaling cutoff dependence that generates these anomalies. Their construction is based on a novel class of Weyl-invariant tensor operators. The only known type A actions in D≥4 are extensions of the Polyakov integral in D=2; despite contrary appearances, we show that their nonlocality does not conflict with general anomaly requirements. They are, however, physically unsatisfactory, prompting a brief attempt at better versions.

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Section: Type Bmentioning

confidence: 99%

Closed form effective conformal anomaly actions in D≥4

Deser

2000

Physics Letters B

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“…The presence of the anomaly is usually encoded in the fact that the boundary energy-momentum tensor acquires an anomalous trace [39][40][41]. Indeed in FG gauge, it is found that it must be a priori traceless.…”

Section: Introductionmentioning

confidence: 99%

Weyl connections and their role in holography

Ciambelli

Leigh

2020

Phys. Rev. D

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It is a well known property of holographic theories that diffeomorphism invariance in the bulk spacetime implies Weyl invariance of the dual holographic field theory in the sense that the field theory couples to a conformal class of background metrics. The usual Fefferman-Graham formalism, which provides us with a holographic dictionary between the two theories, breaks explicitly this symmetry by choosing a specific boundary metric and a corresponding specific metric ansatz in the bulk. In this paper, we show that a simple extension of the Fefferman-Graham formalism allows us to sidestep this explicit breaking; one finds that the geometry of the boundary includes an induced metric and an induced connection on the tangent bundle of the boundary that is a Weyl connection (rather than the more familiar Levi-Civita connection uniquely determined by the induced metric). Properly invoking this boundary geometry has far-reaching consequences: the holographic dictionary extends and naturally encodes Weyl-covariant geometrical data, and, most importantly, the Weyl anomaly gains a clearer geometrical interpretation, cohomologically relating two Weyl-transformed volumes. The boundary theory is enhanced due to the presence of the Weyl current, which participates with the stress tensor in the boundary Ward identity.

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“…means "trivial total derivatives" (as opposed to G 6 , which is a non-trivial total derivative). Our notation differs from the one of [13] in the signs of R µν and R. More importantly, the invariant I 3 differs from the invariant M 3 of [13] and other references [15], the latter containing a spurious contribution proportional to G 6 (see also [3], section 3), as well as a linear combination of I 1 and I 2 . Precisely, we find…”

mentioning

confidence: 97%

Towards the classification of conformal field theories in arbitrary even dimension

Anselmi¹

2000

Physics Letters B

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I identify the class of even-dimensional conformal field theories that is most similar to two-dimensional conformal field theory. In this class the formula, elaborated recently, for the irreversibility of the renormalization-group flow applies also to massive flows. This implies a prediction for the ratio between the coefficient of the Euler density in the trace anomaly (charge a) and the stress-tensor two-point function (charge c). More precisely, the trace anomaly in external gravity is quadratic in the Ricci tensor and the Ricci scalar and contains a unique central charge. I check the prediction in detail in four, six and eight dimensions, and then in arbitrary even dimension.

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Trace Anomalies and Cocycles of Weyl and Diffeomorphisms Groups

Cited by 29 publications

References 6 publications

Closed form effective conformal anomaly actions in D≥4

Closed form effective conformal anomaly actions in D≥4

Weyl connections and their role in holography

Towards the classification of conformal field theories in arbitrary even dimension

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