Modular Flow of Celestial Conformal Field Theory

We first review the calculations for the modular flow and the vector flow of ${\text{CFT}}_2$, warped CFTs and Bondi-Metzner-Sachs Field Theories (BMSFTs), and then we present the vector flows and modular flows in Celestial field theory and Klein CFTs. We also discuss the search for this structure in Lifshitz and other exotic field theories.