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marcus

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The Wikipedia article on Conformal Gravity encourages skepticism about its usefulness

http://en.wikipedia.org/wiki/Conformal_gravity

On the other hand Mannheim may have countered some of the objections to it.

http://arxiv.org/abs/0707.2283

Philip D. Mannheim

8 pages. Proceedings write-up of talk presented at PASCOS-07, Imperial College London, July 2007

(Submitted on 16 Jul 2007)

"The cosmological constant problem and the compatibility of gravity with quantum mechanics are the two most pressing problems in all of gravitational theory. While string theory nicely addresses the latter, it has so far failed to provide any compelling solution to the former. On the other hand, while conformal gravity nicely addresses the cosmological constant problem (by naturally quenching the amount by which the cosmological constant gravitates rather than by quenching the cosmological constant itself), the fourth order derivative conformal theory has long been thought to possess a ghost when quantized. However, it has recently been shown by Bender and Mannheim that not only do theories based on fourth order derivative equations of motion not have ghosts, they actually never had any to begin with, with the apparent presence of ghosts being due entirely to treating operators which were not Hermitian on the real axis as though they were. When this is taken care of via an underlying PT symmetry that such theories are found to possess, there are then no ghosts at all and the S-matrix is fully unitary. Conformal gravity is thus advanced as a fully consistent four-dimensional alternative to ten-dimensional string theory."

http://en.wikipedia.org/wiki/Conformal_gravity

On the other hand Mannheim may have countered some of the objections to it.

http://arxiv.org/abs/0707.2283

**Conformal Gravity Challenges String Theory**Philip D. Mannheim

8 pages. Proceedings write-up of talk presented at PASCOS-07, Imperial College London, July 2007

(Submitted on 16 Jul 2007)

"The cosmological constant problem and the compatibility of gravity with quantum mechanics are the two most pressing problems in all of gravitational theory. While string theory nicely addresses the latter, it has so far failed to provide any compelling solution to the former. On the other hand, while conformal gravity nicely addresses the cosmological constant problem (by naturally quenching the amount by which the cosmological constant gravitates rather than by quenching the cosmological constant itself), the fourth order derivative conformal theory has long been thought to possess a ghost when quantized. However, it has recently been shown by Bender and Mannheim that not only do theories based on fourth order derivative equations of motion not have ghosts, they actually never had any to begin with, with the apparent presence of ghosts being due entirely to treating operators which were not Hermitian on the real axis as though they were. When this is taken care of via an underlying PT symmetry that such theories are found to possess, there are then no ghosts at all and the S-matrix is fully unitary. Conformal gravity is thus advanced as a fully consistent four-dimensional alternative to ten-dimensional string theory."

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