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

Abstract

In a toy model of gauge and gravitational interactions in $D \ge 4$ 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, $α_g \equiv g^2 Λ^{D-4}$ and $α_G \equiv G_N Λ^{D-2}$, are shown to be bounded by appropriate powers of ${1\over N}$. 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.