Observations on conformal anomalies

“…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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“…It is characterized by the following time-reversal symmetric equations: 9) where f (r) is a quantity of order one and varies slowly compared with l p , and l and k are the radial outgoing and ingoing null vectors, respectively:…”

Section: Determination Of A(r) and B(r)mentioning

confidence: 99%

Phenomenological description of the interior of the Schwarzschild black hole

Kawai

Yokokura

2015

Int. J. Mod. Phys. A

107

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We discuss a sufficiently large 4-dimensional Schwarzschild black hole which is in equilibrium with a heat bath. In other words, we consider a black hole which has grown up from a small one in the heat bath adiabatically. We express the metric of the interior of the black hole in terms of two functions: One is the intensity of the Hawking radiation, and the other is the ratio between the radiation energy and the pressure in the radial direction. Especially in the case of conformal matters we check that it is a self-consistent solution of the semi-classical Einstein equation, G µν = 8πG T µν . It is shown that the strength of the Hawking radiation is proportional to the c-coefficient, that is, the coefficient of the square of the Weyl tensor in the 4-dimensional Weyl anomaly. †

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Observations on conformal anomalies

Cited by 539 publications

References 14 publications

The dilaton Wess-Zumino action in higher dimensions

The dilaton Wess-Zumino action in higher dimensions

Lifshitz scale anomalies

Phenomenological description of the interior of the Schwarzschild black hole

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