Twenty years of the Weyl anomaly

Duff, M. J.

doi:10.1088/0264-9381/11/6/004

Cited by 583 publications

(725 citation statements)

References 122 publications

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“…Then it should be a action of Weyl-invariant dilaton gravity, described in Sec. (2.1), because the gauge laws for D ′ , g ′mn just coincide with those of (29). The result is…”

Section: Calculationmentioning

confidence: 80%

Conformal higher spin theory

2003

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We construct gauge theory of interacting symmetric traceless tensors of all ranks s = 0, 1, 2, 3, ... which generalizes Weyl-invariant dilaton gravity to the higher spin case, in any dimension d > 2. The action is given by the trace of the projector to the subspace with positive eigenvalues of an arbitrary hermitian differential operatorĤ, and the symmetric tensors emerge after expansion of the latter in power series in derivatives. After decomposition in perturbative series around conformally flat pointĤ = 2 with Euclidean metric, the action functional describes conformal higher spin theory. Namely, the linear in fluctuation term cancels, while the one quadratic in fluctuation breaks up as a sum of conformal higher spin theories, the latter being free gauge theories of symmetric traceless tensors of rank s with with the algebra of observables of the quantized point particle. Each global symmetry produces a Noether current constructed out of ψ according to general formula we present in the paper. In the caseĤ = 2 the algebra of observables is an extension of the conformal algebra decomposed w.r.t. its adjoint action as a direct sum of finite-dimensional representations characterized by traceless rectangular two-row Young tableaux. This infinite-dimensional algebra coincides, in d = 3, 4, 6 with conformal higher spin algebras constructed before in terms of even spinor oscillators, which origin is due to twistor reformulation of the dynamics of the massless particle. The construction of the paper may be a starting point for diverse conjectures. First, we discuss the extension of the geometry "quantized point particle + conformal higher spin fields in d dimensions" to the one "tensionless d − 1 brane + higher spin massless fields in d + 1 dimensions", where the phase of ψ appear to describe transverse motion of the brane inside d + 1-bulk. This picture arises in the semiclassical approximation to the quantized particle dynamics, the latter approximation provides d-dimensional generalization of W -geometry elaborated on by Hull in d = 1, 2 case. Next, we propose a candidate on the role of Higgs-like higher spin compensator able to spontaneously break higher spin symmetries. At last, we make the conjecture that, in even dimensions d, the action of conformal higher spin theory equals the logarithmically divergent term of the action of massless higher spin fields on AdS d+1 evaluated on the solutions of Dirichlet-like problem, where conformal higher spin fields are boundary values of massless higher spin fields on AdS d+1 , the latter conjecture conforms with recent proposal (for d = 4) by Tseytlin and provides information on the full higher spin action in AdS d+1 .

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“…Then it should be a action of Weyl-invariant dilaton gravity, described in Sec. (2.1), because the gauge laws for D ′ , g ′mn just coincide with those of (29). The result is…”

Section: Calculationmentioning

confidence: 80%

Conformal higher spin theory

2003

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“…Here, we will need in addition to introduce the foliation data. This is a generalization of trace anomalies [11][12][13][14][15]. The latter have attracted a renewed interest recently in relation to the four-dimensional a theorem [16] generalization of the two-dimensional c-theorem [17].…”

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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“…As already pointed out in ref. [121], the problem occurs for uniform rescalings when the conformal factor is a constant, i.e. proportional to the zero mode: in this case even the formula g µν δS [ , where σ is a constant, does not apply, a counterexample being the induced gravity functional (A.19) which is invariant under uniform rescalings but whose metric variation gives rise to the anomaly proportional to R.…”

Section: A2 the Treatment Of Zero Modesmentioning

confidence: 99%

The unitary conformal field theory behind 2D Asymptotic Safety

Nink

Reuter

2016

J. High Energ. Phys.

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Being interested in the compatibility of Asymptotic Safety with Hilbert space positivity (unitarity), we consider a local truncation of the functional RG flow which describes quantum gravity in d > 2 dimensions and construct its limit of exactly two dimensions. We find that in this limit the flow displays a nontrivial fixed point whose effective average action is a non-local functional of the metric. Its pure gravity sector is shown to correspond to a unitary conformal field theory with positive central charge c = 25. Representing the fixed point CFT by a Liouville theory in the conformal gauge, we investigate its general properties and their implications for the Asymptotic Safety program. In particular, we discuss its field parametrization dependence and argue that there might exist more than one universality class of metric gravity theories in two dimensions. Furthermore, studying the gravitational dressing in 2D asymptotically safe gravity coupled to conformal matter we uncover a mechanism which leads to a complete quenching of the a priori expected Knizhnik-Polyakov-Zamolodchikov (KPZ) scaling. A possible connection of this prediction to Monte Carlo results obtained in the discrete approach to 2D quantum gravity based upon causal dynamical triangulations is mentioned. Similarities of the fixed point theory to, and differences from, non-critical string theory are also described. On the technical side, we provide a detailed analysis of an intriguing connection between the Einstein-Hilbert action in d > 2 dimensions and Polyakov's induced gravity action in two dimensions.

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Twenty years of the Weyl anomaly

Cited by 583 publications

References 122 publications

Conformal higher spin theory

Conformal higher spin theory

Lifshitz scale anomalies

The unitary conformal field theory behind 2D Asymptotic Safety

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