Minimal submanifolds asymptotic to AdS 4 × S 2 in AdS 5 × S 5

Abstract

In this work, as an attempt in understanding the interplay between deformations of the external and internal spaces associated with the probe-brane embedding submanifold, we construct the zero-temperature phase diagram for the coupled phase between two two-dimensional defects stacked parallel in a four-dimensional ambient spacetime. Different UV parameters are turned on for different defects. We characterize this solution by its infrared geometric data, and present the numerical result showing a firstorder phase transition between the asymmetrically coupled phase and the more mundane decoupled phase.

Minimal area submanifolds in AdS × compact

“…For general l one has to resort to numerics to construct θ(r), as has recently been carried out in [17] for k = 3, l = 2.…”

“…It is straightforward to integrate the equations of motion numerically, once the smoothness condition in the IR is properly implemented. Explicit examples and a full phase diagram of these configurations, in particular addressing the question whether the connected or the disconnected configuration has the smaller area, have been presented in [17]. One interesting new phenomenon that occurs in these examples is that for a certain range of local boundary data more than one connected regular minimal area exists, that is the global terms aren't unique but can be chosen from a discrete family.…”