Exotic Scalar States in the AdS/CFT Correspondence

Abstract

We investigate a family of solutions of Type IIb supergravity which asymptotically approach AdS_5 X S^5 but contain a non-constant dilaton and volume scalar for the five-sphere. These solutions preserve an SO(1,3) X SO(6) symmetry. We discuss the solution in the context of the AdS/CFT correspondence, and we find that as well as running coupling from the nontrivial dilaton, the corresponding field theory has no supersymmetry and displays confinement at least for a certain range of parameters.

Figures (3)

• Figure 1: Plot of ${r_{min}}/{L}$ (vertical axis) versus $\delta$. Here $L$ is the characteristic curvature scale of the asymptotic AdS region, given by eq. (\ref{['length']}). Note that as $\delta$ approaches zero, $r_{min}$ is getting large and as $\delta\rightarrow \sqrt{5}$, $r_{min}\rightarrow 0$.
• Figure 2: Plot of $L^2(\nabla\phi (r_{min}))^2$ (vertical axis) versus $\delta$. Here $\phi (r)$ is the background dilaton (\ref{['dilaton']}), and $L$ is the asymptotic AdS scale (\ref{['length']}). The figure suggests that the $\alpha^{\prime}$ expansion is breaking down at $r_{min}$ for $\delta>2$.
• Figure 3: Plot of the $e^{\phi(r_{min}) - \phi_{0}}$ (vertical axis) versus $\delta$. The vertical axis gives ratio of the string coupling evaluated at $r_{min}$ to that in the asymptotic AdS region. The plot is made for positive ${\mit \Delta}=\sqrt{10-\delta^2}$ in eq. (\ref{['dilaton']}). In this case, the figure suggests that the string loop expansion will become uncontrolled for $\delta > 2$.