Large-N bounds on, and compositeness limit of, gauge and gravitational interactions

In a toy model of gauge and gravitational interactions in D ≥ 4 dimensions, endowed with an invariant UV cut-off Λ, and containing a large number N of non-self-interacting matter species, the physical gauge and gravitational couplings at the cut-off, αg ≡ gΛ and αG ≡ GNΛ, are shown to be bounded by appropriate powers of 1 N . This implies that the infinite-bare-coupling (so-called compositeness) limit of these theories is smooth, and can even resemble our world. We argue that such a result, when extended to more realistic situations, can help avoid large-N violations of entropy bounds, solve the dilaton stabilization and GUT-scale problems in superstring theory, and provide a new possible candidate for quintessence. CERN-TH/2001-278 October 2001 1 The toy model and the claim Consider a toy model of gauge and gravitational interactions inD ≥ 4 space-time dimensions, minimally coupled to a large number of spin 0 and spin 1/2 matter fields. Let us endow the model with a cut off Λ, assumed to be finite and to preserve gauge invariance and general covariance. The toy model is supposed to mimic a bona-fide higher dimensional UV-finite theory of all interactions such as those provided by superstring theory. Let us also neglect, for the moment, matter self interactions. The tree-level action of the model thus reads, in obvious notations S0 = − 1 2 ∫