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We prove global existence and stability of solution to the mass-criticalstochastic nonlinear Schr\"odinger equation in $d=1$ at $L^2$ regularity. Ourconstruction starts with the existence of solution to the truncated subcriticalproblem. With the presence of truncation, we construct the solution to thecritical equation as the limit of subcritical solutions. We then obtain uniformbounds on the solutions to the truncated critical problems that allow us toremove truncation in the limit.

Global well-posedness for the defocusing mass-critical stochastic nonlinear Schr\"odinger equation on $\mathbb{R}$ at $L^2$ regularity