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As described in "A class of elementary particle models without any adjustable real parameters", "The Conformal Constraint in Canonical Quantum Gravity", and "Probing the small distance structure of canonical quantum gravity using the conformal group". (Also see "Quantum gravity without space-time singularities or horizons".)

The motivating idea is that black hole complementarity is implemented by conformal transformations. This leads to an interest in theories of gravity+matter which possess an exact local scale invariance, spontaneously broken by a dilaton VEV. In order to avoid a particular divergence, it's suggested that the dilaton has nontrivial couplings to the matter fields, such that the beta function vanishes. Therefore, the coupling constants of such a theory are not free parameters; they must satisfy this "conformal constraint".

No concrete examples of such a theory are provided, but the papers do contain some reasoning about relations between the physical constants, such as the implications of a small nonzero cosmological constant.

I would appreciate any intelligent commentary on these papers, but especially from the perspective of string theory. For example, the whole process reminds me a little of what would be involved in constructing a worldvolume Lagrangian for a supermembrane (except that supersymmetry is playing no role here).

But I am also suspicious of theoretical approaches which say "such a theory wouldn't work unless all the natural constants cooperate to produce a miracle, therefore such a theory would predict all the natural constants, but I don't have a concrete example of such a theory". In the absence of quantitative evidence that nontrivial examples of the "miracle" exist, I am inclined to think that the required miracle is either impossible or unnecessary. After all, the opportunity for the miracle to appear and produce a predictive theory, only occurs after a series of guesses about how the theory should work. If one of these presupposed guesses is wrong, then we are dealing with a mirage, not a miracle.

However, it would be better to have an opinion that engaged with some of the technicalities in these papers, rather than just being based on high-level heuristics. So: Is this new landscape real? Is it relevant? Does it overlap with the string landscape?

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