Naive Dimensional Analysis in Holography

TL;DR

This paper uses gauge/string duality to test and extend naive dimensional analysis (NDA) for estimating glueball couplings in strongly coupled gauge theories, confirming NDA's scaling rules and broadening its applicability.

Contribution

It verifies and extends NDA scaling rules for glueball couplings using holographic methods, applicable to a wider class of gauge theories.

Findings

NDA scaling rule for glueball couplings is validated.

Numerical calculations support the NDA estimates.

The scaling rule applies to quiver gauge theories as well.

Abstract

Naive dimensional analysis (NDA) is a widely used ansatz to estimate coupling constants among composite states emerging from dynamics of a strongly coupled gauge theory. However, the validity of NDA is still unclear because of the difficulty in calculating these quantities in strongly coupled theories. We examine the NDA ansatz using gauge/string duality, by estimating glueball coupling constants from gravitational description. The NDA scaling rule for coupling constants of some types of glueballs is verified and extended by both generic estimation and numerical calculations. The scaling rule verified in this article can be applied to some class of quiver gauge theories as well, not just to gauge theories with a single gauge group $SU(N_c)$.