First we need to discuss what is meant by a boundary.

Consider a rectangular sheet of paper. The boundary of the whole sheet is a rectangle, the edge of the paper. It's where the paper ends.

Now draw a circle on the sheet of paper. The circle is the boundary of a disk-shaped region of paper inside the circle, but the paper doesn't stop there. This boundary has an outside as well as an inside.

The firewall, if it existed, would be like the boundary of the circle. But holographic duality involves the edge of the paper. The dual field theory describes everything on the sheet of paper, not just what happens inside the circle.

This post imported from StackExchange Physics at 2014-03-07 13:38 (UCT), posted by SE-user Mitchell Porter