On Asymptotic Freedom and Confinement from Type-IIB Supergravity

TL;DR

The paper constructs new type-IIB supergravity vacua to model strong-coupling dynamics of non-supersymmetric gauge theories with UV asymptotic freedom and a running theta angle. It analyzes both a non-supersymmetric solution and a supersymmetric interpolating background, examining their geometric and holographic properties and computing observables such as the quark-antiquark potential through Wilson loops. A key result is that the non-supersymmetric vacuum yields a running 't Hooft coupling $g_H$ that vanishes in the UV, while the supersymmetric solution yields an ${\cal N}=2$ SYM with running coupling and a finite-action wormhole-like interpolation between flat space and $AdS_5\times S^5$; the Wilson-loop analysis reveals Coulombic behavior at short distances and, under certain conditions, an area-law (linear confinement) regime with a mass gap. The work provides a holographic framework for studying confinement and running couplings in gauge theories via type-IIB supergravity, including a wormhole-type vacuum with two asymptotic regions.

Abstract

We present a new type-IIB supergravity vacuum that describes the strong coupling regime of a non-supersymmetric gauge theory. The latter has a running coupling such that the theory becomes asymptotically free in the ultraviolet. It also has a running theta angle due to a non-vanishing axion field in the supergravity solution. We also present a worm-hole solution, which has finite action per unit four-dimensional volume and two asymptotic regions, a flat space and an AdS^5\times S^5. The corresponding N=2 gauge theory, instead of being finite, has a running coupling. We compute the quark-antiquark potential in this case and find that it exhibits, under certain assumptions, an area-law behaviour for large separations.

Figures (1)

• Figure 1: Plot of the quark--antiquark potential in (\ref{['qbqrq']}) as a function of the separation distance $L$, in units of $a=(2 \eta_1 R^2)^4$. For small $L$ we have a Coulombic behaviour, whereas it is linear for large $L$.