Abstract

Classical error correcting codes are related to special lattices, which give rise to chiral CFTs. Recently this story was generalized to non-chiral theories. In this case quantum codes give rise to Narain lattices and a special family of Narain theories which we dub code CFTs. Some of these code theories maximize the spectral gap, making connection with the conformal bootstrap program. From the holographic point of view, code CFTs form an ensemble which provides a simplified model for the recently introduced duality between ensembles of boundary theories and quantum gravity in the bulk. In this talk I will first describe the mapping between quantum codes and Narain theories, and then discuss examples of optimal CFTs which maximize the spectral gap. In the second part of the talk I will discuss the ensemble of code theories and several lessons they presumably teach us about the ensemble of all Narain theories and its holographic description.