Dual PT-symmetric quantum field theories

Some quantum field theories described by non-Hermitian Hamiltonians are investigated. It is shown that for the case of a free fermion field theory with a γ5 mass term the Hamiltonian is PT-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the PT symmetry is unbroken, the spectrum of the quantum field theory is real. For the PT-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the PT-symmetric scalar sine-Gordon model, an exact construction of the C operator is given. It is shown that the PT-symmetric massive Thirring and sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and sine-Gordon models with appropriately shifted masses.