In a recent thread, marcus brought my attention to 't Hooft's Quantum gravity without space-time singularities or horizons http://arxiv.org/abs/0909.3426 .(adsbygoogle = window.adsbygoogle || []).push({});

For emergent gravity, the major no-go theorem is the Weinberg-Witten theorem, which string theory gets round apparently by having space emerge with gravity. In a footnote of their paper, Weinberg and Witten state "The theorem does not apply to theories in which the gravitational field is a basic degree of freedom, but the Einstein action is induced by quantum effects" (Is this why Wen has been making cryptic remarks about long range entanglement?) They go on to list a bunch of theories which aren't excluded by their theorem, which includes, in addition to Sakharov's original induced gravity and many others:

Towards a theory of spacetime structure at very short distances

Lee Smolin

Nuclear Physics B 160: 253-268, 1979

Renormalization-group arguments are summarized which suggest that at distances shorter than the Planck length the spacetime geometry should be asymptotically scale invariant. A new locally scale-invariant extension of general relativity is then proposed based on Weyl's conformally invariant geometry. It is shown that if the theory contains a Higgs phase, then it reduces to Einstein's theory in the limit of large distances. Finally, the theory incorporates the non-linear sigma model, which suggests a new approach to the calculation of non-perturbative, short-distance effects in quantum gravity.

OK, I'm free associating here between a paper I don't understand at all ('t Hooft's) and another I haven't read (can't seem to get Smolin's paper free). While I'm at it, let me also bring up Strominger's comment in http://arxiv.org/abs/0906.1313: "If gravity is induced, which means that Newton’s constant is zero at tree level and arises as a one loop correction, then the entanglement entropy is responsible for all of the entropy, and reproduces the area law with the correct coefficient. This might in fact be the case in string theory, where the Einstein action is induced at one loop from open strings, but this notion has yet to be made precise. Recent progress has revealed a rich holographic relation between entanglement entropy and minimal surfaces including horizons."

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# Smolin's emergent gravity

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