# Holographic dual of a massive QFT?

A naive question about holographic dual of a massive QFT: The Ryu-Takanayagi formula for the entanglement entropy (see their paper) seem to suggest that the holographic dual of a massive QFT (e.g. a CFT, which has a good holographic dual, perturbed by a relevant perturbation) is a "capped off" AdS, so I'd like to know what the precise meaning of "capped off" AdS is? For example, a concrete metric?

Any comments or references are welcome, thank you.

For a mass perturbed CFT below the mass scale, the mass gap prevents pair creation and the field theory "freezes out". This can be (roughly) modelled via AdS/CFT by capping of the holographic coordinate (and thus the spacetime) and restrict it to some range $0<z<z_0$, as everything that happens beyond $z_0$ cannot affect the mass deformed theory.
The entanglement entropy is of course altered by the deformation as pair produced particles are ultimately responsible for this entropy. The Ryu-Takayanagi formula $$S=\frac{A}{4 G_N}$$ can capture this reduction of entanglement by cutting off the bulk homologous surfaces (ending on the entangling region on on the boundary) and thus reducing the surface area.
• Thanks, one more question related: if we assume there is a space termination at $z_0$, in order to satisfy the Einstein equation, do we need a boundary condition, say, a massive membrane at $z=z_0$? How to understand that in holography? What's the dual object in QFT? – Yingfei Gu Jun 25 '15 at 16:34
• I don't think people usually put boundary conditions such that the Einstein equations are satisfied. One simply takes a solution of Einstein's equations without cap off and caps off afterwards resulting in a spacetime, that obviously does not satisfy Einstein's equations. This is why I said the process is not well-defined. One only sets boundary conditions for the non-gravitational field, namely other fields have to vanish at $z_0$. – physicus Jun 25 '15 at 16:44