  The Parity-Time $\mathcal{PT}$-symmetric non-Hermitian Sine-Gordon(nhSG)
model derived from the nonequilibrium spin-boson model. We have derived the
Keldysh rotation for spin operators, from which the SG model can be derived. We
perform renormalization group calculations in the Keldysh fields and compare
the fixed points and the flow of the effective couplings of nonequilibrium and
non-Hermitian models. Also, we explicitly find the self-energies and compare
the two methods to understand the regimes where $\mathcal{PT}$ symmetry
preserved regime, and nonequilibrium regimes persist.RG flow of couplings of
nonequilibrium model and non-hermitian model both capture the standard
Berezinskii-Kosterlitz-Thouless(BKT) physics in a strong coupling regime.
