Abstract:Globular clusters (GCs) are long-lasting survivors of galaxy assembly and evolution, yet the processes behind their emergence from an initial cluster population are still poorly constrained. Here, we present Auriga GLOBular clustEr Simulations (AuriGLOBES) a physically motivated subgrid model for star cluster (SC) formation and evolution that includes enhanced mass loss from compact object remnants. With this model, implemented in the Auriga cosmological galaxy formation model, we ran a suite of zoom-in cosmological simulations comprising nine Milky Way (MW) mass and five lower mass galaxies. We demonstrate that our model produces plausible GC populations, compared to the MW/M31 systems, and reproduces the empirical GC system-mass-halo-mass relation within a 2$\sigma$ scatter. We show that the formation of SCs in tidally compressive, high-pressure gas in addition to enhanced mass loss from compact object remnants heating is required to capture the transformation of an initial Schechter mass function to the characteristic observed GC mass function in the MW/M31 systems. The resulting GC populations exhibit spatial and metallicity distributions that are qualitatively similar to the MW/M31 systems, as well as a variety of age distributions that correlate with the star formation history of the simulated galaxies. However, the peak of the age distribution of MW GCs is older than any of our simulated MW-mass galaxies, which is attributed to unrepresented star formation and galaxy assembly histories. AuriGLOBES represents a reliable framework for the study of GC populations through cosmic history and offers a robust foundation for future applications in modelling stellar streams arising from GC disruption.