A Dilatonic Deformation of AdS_5 and its Field Theory Dual

TL;DR

The authors construct a nonsupersymmetric but exact dilatonic deformation of AdS5 that is regular and asymptotically AdS5, introducing a spatially varying dilaton that creates two boundary halves with different gauge couplings across a codimension-one defect. This yields a defect conformal field theory in the AdS/CFT framework, with the dilaton coupling jump encoding the boundary YM coupling and preserving SO(3,2) while breaking part of Lorentz symmetry. They analyze the boundary geometry, compute Wilson loops in the deformed background, and show perturbative stability against scalar fluctuations, providing a concrete gravity dual for a dCFT without bulk branes. The work also draws parallels and contrasts with Karch-Randall constructions, offering a simple explicit example of a defect holography and suggesting avenues for generalizations and backreaction studies.

Abstract

We find a nonsupersymmetric dilatonic deformation of $AdS_5$ geometry as an exact nonsingular solution of the type IIB supergravity. The dual gauge theory has a different Yang-Mills coupling in each of the two halves of the boundary spacetime divided by a codimension one defect. We discuss the geometry of our solution in detail, emphasizing the structure of the boundary, and also study the string configurations corresponding to Wilson loops. We also show that that the background is stable under small scalar perturbations.

Figures (8)

• Figure 1: The dynamics corresponds to the particle motion under a potential with zero energy. We depict the shape of the potential here. We are interested in the trajectory in which the particle starts from infinity, reflected at $f_{min}$ and goes back to infinity.
• Figure 2: $f(\mu)$ as a function of $\mu$ for values of $c_0= 0.2, 0.8,1.3$
• Figure 3: The range of the coordinate $\mu$ as a functions of $c_0$, where $c_0$ varies from $0$ to $c_{crit}= {9\over 4\sqrt{2}}$, $\mu_0$ starts from $\mu_0={\pi\over 2}$ and diverges at $c_0=c_{crit}$
• Figure 4: The dilaton $\phi$ as a functions of $\mu$, for values of $c_0= 0.2,\; .8, \; 1.3$
• Figure 5: The range of the dilaton $\phi$ as a function of $c_0$, the range of the dilaton diverges at $c_0=c_{crit}$