$T\bar{T}$ deformation on non-Hermitian two coupled SYK model

Abstract: We investigate $T\bar{T}$ deformation on non-Hermitian coupled Sachdev-Ye-Kitaev (SYK) model and the holographic picture. The relationship between ground state and thermofield double state is preserved under the $T\bar{T}$ deformation. We prove that $T\bar{T}$ deformed theory provides a reparameterization in large $N$ limit. These deformation effects is calculated numerically with green functions and free energy. The thermodynamic phase structures show the equivalence of the wormhole-black hole picture between non-Hermitian model and Hermitian model still holds under $T\bar{T}$ deformation. We also study the correlation function in Lorentz time and revival dynamic.