What a PT!

It has been shown that there exists a set of non-Hermitian theories which may describe a physical system. Those enjoy an antilinear symmetry, usually denoted PT, and have a real spectrum which is bounded from below. We shall review the basic features of such theories and discuss how to implement them holographically. We will also address the question of time evolution. When driven by the usual Schrödinger equation the evolution is not unitary. This shows up holographically as a shrinking apparent horizon and the violation of the Null Energy Condition in the bulk. Alternatively, the evolution can be made unitary by modifying the Schrödinger equation, which is equivalent to switching on a gauge field in the bulk.