On an exotic Lagrangian torus in $\mathbb{C}P^2$

Abstract

We find a non-displaceable Lagrangian torus fiber in a semi-toric system, which is superheavy with respect to certain symplectic quasi-state. In particular, this proves Lagrangian $\RR P^2$ is not a stem in $\CC P^2$, answering a question of Entov and Polterovich.