Deconfinement and Error Thresholds in Holography

We study the error threshold properties of holographic quantum error-correcting codes in the context of the AdS/CFT correspondence. We demonstrate that holographic conformal field theories admit an algebraic threshold, which is related to the confinement-deconfinement phase transition. We then apply geometric intuition from holography and the Hawking-Page phase transition to motivate the conformal field theory result, and comment on potential extensions to other confining theories. In particular, we show that the corruption of logical information above the threshold can be seen as information being engulfed by a black hole in the dual holographic spacetime in one higher dimension.