A light scalar from walking solutions in gauge-string duality

TL;DR

The paper investigates whether approximate infrared scale invariance in strongly coupled gauge theories implies a light dilaton by analyzing a Type-IIB background from D5 branes wrapped on S^2 that exhibits a walking regime. It constructs walking solutions via a master equation for $P(\rho)$, reduces to a 5D nonlinear sigma model with six scalars, and analyzes scalar fluctuations to extract the glueball spectrum using IR–UV matching and boundary conditions reflecting UV branch cuts at $M^2>1$ and $M^2>9$. The key result is the existence of one isolated scalar whose mass is parametrically suppressed by the walking length and tends to zero as $\rho_*\to\infty$, consistent with a dilaton-like pseudo-Goldstone of dilatations. This work provides a calculable framework to study dilaton dynamics in walking theories and offers guidance for phenomenological model building.

Abstract

We consider the type-IIB background generated by the strong-coupling limit of Nc D5 branes wrapped on S2, and focus our attention on a special class of solutions that exhibit walking behavior. We compute numerically the spectrum of scalar fluctuations around vacua of this class. Besides two cuts, and sequences of single poles converging on one of the branch points, the spectrum contains one isolated scalar, the mass of which is suppressed by the length of the walking region. Approximate scale-invariance symmetry in the walking region suggests that this be interpreted as a light dilaton, the pseudo-Goldstone boson of dilatations.

Figures (3)

• Figure 1: Examples of solutions to Eq. (\ref{['master']}) which fall into the class with walking behavior, compared to $\hat{P}=2N_c \rho$.
• Figure 2: The gauge coupling $\lambda$ defined in the text, as a function of the radial coordinate, for the same solutions as in Fig. \ref{['Fig:solutions']}.
• Figure 3: The masses $M^2$ plotted against $P_0/N_c \simeq 2\rho_{\ast}$.