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

TL;DR

Veneziano examines a higher-dimensional toy model with a finite UV cutoff $\Lambda$ and a large number of matter species to derive bounds on the physical gauge and gravitational couplings at the cutoff, namely $\alpha_g < c_1/N^p$ and $\alpha_G < c_2/N$ with $D>4$ (gauge) or $D\ge4$ (gravity). The proof relies on integrating out matter fields to obtain the one-loop–dominated effective action via heat-kernel methods, yielding saturation of the bounds in the compositeness limit and a smooth infinite-bare-coupling regime. The results have potential implications for entropy bounds, dilaton stabilization and GUT-scale issues in string theory, and they motivate a possible quintessence role for a runaway dilaton. If these large-$N$ insights extend to realistic theories, they provide a mechanism for high-energy coupling suppression tied to the matter content, with implications for fundamental scales.

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.