  We obtain global well-posedness, scattering, and global $L_t^4H_{x}^{1,4}$
spacetime bounds for energy-space solutions to the energy-subcritical nonlinear
Schr\"odinger equation \[iu_t+\Delta u=u(e^{4\pi |u|^2}-1)\] in two spatial
dimensions. Our approach is perturbative; we view our problem as a perturbation
of the mass-critical NLS to employ the techniques of Tao--Visan--Zhang. This
permits us to combine the known spacetime estimates for mass-critical NLS
proved by Dodson and the work of Ibrahim--Majdoub--Masmoudi--Nakanishi on a
related problem to prove corresponding spacetime estimates which imply
scattering.
