Traditionally a Hamiltonian is taken to be a Hermitian operator on Hilbert space. It is however well-known that certain non-Hermitian operators give rise to meaningful quantum mechanics. This is the subject of PT-symmetric quantum mechanics. I will review the physical meaning and mathematical construction of such Hamiltonians. Then I will present a new holographic model that can be viewed as dual to a strongly coupled PT-symmetric quantum field theory. A particular emphasis will be given on the PT-phase transition at zero and finite temperature.
