Topic

# Conformal gravity

About: Conformal gravity is a research topic. Over the lifetime, 1192 publications have been published within this topic receiving 29162 citations.

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TL;DR: The coupling of conformal field theories to 2-d gravity may be studied in the conformal gauge as mentioned in this paper, where the results of Knizhnik, Polyakov, and Zamolodchikov for the scaling dimensions of the field are derived in a simple way.

Abstract: The coupling of conformal field theories to 2-d gravity may be studied in the conformal gauge. As an application, the results of Knizhnik, Polyakov and Zamolodchikov for the scaling dimensions of conformal fields are derived in a simple way. Their conjecture for the susceptibility exponent γ of strings is proven and extended to arbitrary genus surfaces. The result agrees with exact results from random lattice models.

1,010 citations

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TL;DR: In this article, the requirements of conformal invariance for two-and three-point functions for general dimension d on flat space are investigated and a compact group theoretic construction of the threepoint function for arbitrary spin fields is presented and it is applied to various cases involving conserved vector operators and the energy momentum tensor.

926 citations

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TL;DR: In this article, it was shown that conformal invariance is broken spontaneously by the vacuum expectation value of an unphysical scalar field; this process induces general relativity as an effective long distance limit.

680 citations

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TL;DR: The embedding formalism for conformal field theories is developed, aimed at doing computations with symmetric traceless operators of arbitrary spin, using an indexfree notation where tensors are encoded by polynomials in auxiliary polarization vectors.

Abstract: We develop the embedding formalism for conformal field theories, aimed at doing computations with symmetric traceless operators of arbitrary spin. We use an index-free notation where tensors are encoded by polynomials in auxiliary polarization vectors. The efficiency of the formalism is demonstrated by computing the tensor structures allowed in n-point conformal correlation functions of tensors operators. Constraints due to tensor conservation also take a simple form in this formalism. Finally, we obtain a perfect match between the number of independent tensor structures of conformal correlators in d dimensions and the number of independent structures in scattering amplitudes of spinning particles in (d+1)-dimensional Minkowski space.

624 citations

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TL;DR: In this paper, the exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented, which includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance.

Abstract: The complete, exact exterior solution for a static, spherically symmetric source in locally conformal invariant Weyl gravity is presented. The solution includes the familiar exterior Schwarzschild solution as a special case and contains an extra gravitational potential term which grows linearly with distance. The obtained solution provides a potential explanation for observed galactic rotation curves without the need for dark matter. The solution also has some interesting implications for cosmology.

589 citations