Dual PT-Symmetric Quantum Field Theories

TL;DR

This paper explores non-Hermitian quantum field theories with PT symmetry, demonstrating conditions for real spectra and establishing equivalences between PT-symmetric and conventional models, including the Thirring and Sine-Gordon models.

Contribution

It provides an analysis of PT symmetry in quantum field theories, constructs the C operator for the PT-symmetric Thirring model, and shows their equivalence to Hermitian models with shifted parameters.

Findings

PT symmetry can be unbroken or broken depending on the mass parameter.

The spectrum of PT-symmetric free fermion theory is real when PT symmetry is unbroken.

PT-symmetric Thirring and Sine-Gordon models are equivalent to their Hermitian counterparts with shifted masses.

Abstract

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 $\gamma_5$ mass term the Hamiltonian is $\cal PT$-symmetric. Depending on the mass parameter this symmetry may be either broken or unbroken. When the $\cal PT$ symmetry is unbroken, the spectrum of the quantum field theory is real. For the $\cal PT$-symmetric version of the massive Thirring model in two-dimensional space-time, which is dual to the $\cal PT$-symmetric scalar Sine-Gordon model, an exact construction of the $\cal C$ operator is given. It is shown that the $\cal PT$-symmetric massive Thirring and Sine-Gordon models are equivalent to the conventional Hermitian massive Thirring and Sine-Gordon models with appropriately shifted masses.