# Thermofield double For a quantum system with energy eigenstates $|\psi_n\rangle$ and energies $E_n$, the thermofield double (TFD) state is a state in the doubled Hilbert space $\mathcal{H}=\mathcal{H}_1 \times \mathcal{H}_2$, and is defined to be$|\mathrm{TFD}\rangle=\frac{1}{\sqrt{Z(\beta)}} \sum_n e^{-\beta E_n / 2}\left|\psi_n\right\rangle_1 \times\left|\psi_n\right\rangle_2.$ In [[0001 AdS-CFT|AdS/CFT]], as argued in [[2001#Maldacena]] using [[0555 Gravitational path integral|gravitational path integral]], a TFD state of two copies of the boundary CFT is dual to the two-sided black hole in the bulk. ## Refs - bulk dual of TFD: [[2001#Maldacena]] - TFD in causal diamonds: [[2023#Chakraborty, Ordonez, Valdivia-Mera]]