On running couplings in gauge theories from type-IIB supergravity

TL;DR

Proposes an explicit Type IIB supergravity background with a non-constant dilaton that yields a running boundary coupling $g_H$ and exhibits a UV-stable fixed point at $g_H^*$. The solution is analyzed via a warp factor $\Omega(\rho)$ and dilaton $\Phi(\rho)$ in a setup preserving $AdS_5$-like asymptotics, with an IR cutoff $\rho_0$ and a universal near-fixed-point beta-function slope. It also computes the first dilaton-induced correction to the quark–antiquark potential, finding a deviation from pure Coulombic scaling (and a corresponding monopole potential under S-duality). These results connect bulk deformations to boundary operator content (marginal and irrelevant operators) and suggest a universal power-law running mechanism in holographic, non-conformal gauge theories.

Abstract

We construct an explicit solution of type-IIB supergravity describing the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling with an ultraviolet stable fixed point corresponding to the N=4 SU(N) super-Yang-Mills theory at large N. The running coupling has a power law behaviour, argued to be universal, that is consistent with holography. Around the critical point, our solution defines an asymptotic expansion for the gauge coupling beta-function. We also calculate the first correction to the Coulombic quark-antiquark potential.

Figures (2)

• Figure 1: Plot of $\Omega(\rho)/R$ in units where $\rho_0=1$. Curves $(1)$ and $(2)$ were plotted using (\ref{['assa']}) and (\ref{['assy1']}) respectively. The curve corresponding to $\Omega(\rho)/R$, obtained by numerically solving (\ref{['sol1']}), coincides with the union of these curves.
• Figure 2: Plot of $g_{\rm H}/g^*_{\rm H}$ as a function of $U$ using (\ref{['runn']}).