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

In a toy model of gauge and gravitational interactions in Dgreater than or equal to4 dimensions, endowed with an invariant UV cut-off Lambda, and containing a large number N of non-self-interacting matter species, the physical gauge and gravitational couplings at the cut-off, alpha(g) equivalent to g(2)Lambda(D-4) and alpha(G) equivalent to G(N)Lambda(D-2), 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.