The fundamental object of Gromov-Witten theory is the notation of stable map to a target Kahler/Symplectic manifold.  In LG A-model in physics, the target carries an additional $C^*$ action called R-charge. It twisted the notation of map in so-called gauged linear sigma model. Furthermore, its moduli space is noncompact even with stability condition. In the talk, we will  introduce the notation of $R$-map. The effort to compactify it leads to the theory of Logarithmic R-maps. This is a joint work with Qile Chen and Felix Janda.