Non-Hermitian quantum quenches in holography

The notion of non-Hermitian PT symmetric quantum theory has recently been gen-eralized to the gauge/gravity duality. We study the evolution of such non-Hermitian holographic field theories when the couplings are varied with time with particular em-phasis on the question non-unitary time vs. unitary time evolution. We show that a non-unitary time evolution in the dual quantum theory corresponds to a violation of the Null Energy Condition (NEC) in the bulk of the asymptotically AdS spacetime. We find that upon varying the non-Hermitian coupling the horizon of a bulk AdS black hole shrinks. On the other hand varying the Hermitian coupling in the presence of a constant non-Hermitian coupling still violates the NEC but results in a growing horizon. We also show that by introducing a non-Hermitian gauge field the time evolution can be made unitary, e.g. the NEC in the bulk is obeyed and an exactly equivalent purely Hermitian description can be given.

Automated summary

The recent generalization of the notion of non-Hermitian PT symmetric quantum theory to the gauge/gravity duality is studied. The evolution of these non-Hermitian holographic field theories when the couplings vary with time is examined, with a focus on the distinction between non-unitary and unitary time evolution. It is found that non-unitary time evolution corresponds to a violation of the Null Energy Condition (NEC) in the bulk of the asymptotically AdS spacetime. Additionally, the variations in non-Hermitian coupling lead to a shrinking horizon of a bulk AdS black hole, while variations in Hermitian coupling, in the presence of a constant non-Hermitian coupling, still violate the NEC but result in a growing horizon. It is demonstrated that introducing a non-Hermitian gauge field allows for unitary time evolution, as the NEC is obeyed in the bulk and an exactly equivalent purely Hermitian description can be provided.