RevModPhys.84.987

Keep in mind not only the barrier for quantum elds in

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Unformatted text preview: e ultraviolet but also in the infrared. Pertinent to this statement is the generalized WeinbergWitten theorem. The assumptions are that (i) the Lorentz minimal coupling term is always present, and (ii) the theory extends to all energies without encountering any infrared or ultraviolet catastrophe. To reiterate, the refined analysis relies crucially via assumption (i) on Weinberg’s formulation of the equivalence principle,18 which one may view as a low-energy constraint on the theory. The result is that massless higherspin particles cannot couple with the universal graviton or anything that the latter couples to. In other words, if such massless higher-spin theories in flat background exist in the mathematical sense, they cannot be engineered to the lowenergy physics that takes place in our Universe. For instance, one can have a theory with two phases: A symmetric phase at high energy where higher-spin particles are massless and the Newton constant vanishes for all particles, and a broken phase, where higher-spin particles get a mass and the Newton constant is nonzero. This is an intriguing possibility; moreover it probably occurs in AdS4 (Girardello, Porrati, and Zaffaroni, 2003); see the discussion in Sec. IV.D. Nothing forbids the existence of an a priori very warm universe where such exotic theories are relevant. After cooling and symmetry breakdown these may then yield an effective matter-coupled gravity theory in which the graviton is that field that couples to everything in always the same way, with a single coupling constant introduced, namely, Newton’s constant. The assumptions (i) and (ii) are indeed vulnerable to the possibility of phase transitions. This will be discussed in Sec. IV.D. Looking to the limits of the experimental as well as theoretical tests of the Lorentz minimal coupling, there is no reason a priori as to why the specific mechanism by which diffeomorphism invariance is implemented in Einstein’s gravity should work at scales that are very small or very large. This suggests that the Lorentz minimal coupling can be rehabilitated within theories with infrared as well as ultraviolet cutoffs. D. Flat background As already stressed, the strict definition of massless particle and S matrix requires a flat spacetime. Passing to a slightly curved de Sitter or anti–de Sitter spacetime with cosmological constant Ã, one sometimes considers the existence of gauge symmetries as the criterion19 of masslessness. Since there is no genuine S matrix in AdS, a subtle and fruitful way out is that the S-matrix theorems do not apply any more when the cosmological constant à is nonvanishing; instead one resorts to a holographic dual conformal field theory. This way out has been exploited successfully by the Lebedev school and has given rise to cubic vertices and full nonlinear equations of motion. E. Finite dimensionality of spacetime Finally, in light of the recent progress made in amplitude calculations in ordinary relativistic quantu...
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