A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
Dual PT-Symmetric Quantum Field Theories
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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.
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Exact solitary waves exist for the generalized PT-symmetric nonlinear Dirac equation with power-law nonlinearity, conserving energy and momentum with the PT transition independent of the nonlinearity exponent and stability restricted by gain-loss and higher nonlinearity.
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Non-Hermitian free-fermion critical systems and logarithmic conformal field theory
A PT-symmetric non-Hermitian free-fermion field theory realizes logarithmic conformal field theory with central charge c=-2 via a biorthogonal Virasoro algebra construction.
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