Entanglement Entropy in Internal Spaces and Ryu-Takayanagi Surfaces

Understand

We study minimum area surfaces associated with a region, $R$, of an internal space.

• For example, for a warped product involving an asymptotically $AdS$ space and an internal space $K$, the region $R$ lies in $K$ and the surface ends on $\partial R$.
• We find that the result of Graham and Karch can be avoided in the presence of warping, and such surfaces can sometimes exist for a general region $R$.
• When such a warped product geometry arises in the IR from a higher dimensional asymptotic AdS, we argue that the area of the surface can be related to the entropy arising from entanglement of internal degrees of freedom of the boundary theory.