``Codes, CFTs, and ensemble holography''

Holographic correspondence is a duality between gravity in (d+1)-dimensional curved AdS space and non-gravitational d-dimensional QFT “living” on the boundary. More recently a substantial evidence emerged that perhaps a more fundamental version of holographic duality would be between gravity in (d+1)-dimensions and a boundary ensemble of many QFTs. Details and microscopic picture behind this duality is still largely unclear. I will show that ensemble duality emerges naturally in the context of the relation between classical and quantum codes and conformal field theories in 2d. This relation was identified back in the 90s and revised recently, leading to surprising connections with higher form symmetries and quantum information. The emerging picture is that boundary CFTs are labeled by quantum codes, such that the statement of holographic duality becomes a quantum information theoretic identity between different families of stabilizer states.