  Galaxy sizes correlate closely with the sizes of their parent dark matter
haloes, suggesting a link between halo formation and galaxy growth. However,
the precise nature of this relation and its scatter remains to be understood
fully, especially for low-mass galaxies. We analyse the galaxy-halo size
relation for low-mass ($M_\star \sim 10^{7-9} {\rm M_\odot}$) central galaxies
over the past 12.5 billion years with the help of cosmological volume
simulations (FIREbox) from the Feedback in Realistic Environments (FIRE)
project. We find a nearly linear relationship between the half-stellar mass
galaxy size $R_{1/2}$ and the parent dark matter halo virial radius $R_{\rm
vir}$. This relation evolves only weakly since redshift $z = 5$: $R_{1/2} {\rm
kpc} = (0.053\pm0.002)(R_{\rm vir}/35 {\rm kpc})^{0.934\pm0.054}$, with a
nearly constant scatter $\langle \sigma \rangle = 0.084 [{\rm dex}]$. Whilst
this ratio is similar to what is expected from models where galaxy disc sizes
are set by halo angular momentum, the low-mass galaxies in our sample are not
angular momentum supported, with stellar rotational to circular velocity ratios
$v_{\rm rot} / v_{\rm circ} \sim 0.15$. Introducing redshift as another
parameter to the GHSR does not decrease the scatter. Furthermore, this scatter
does not correlate with any of the halo properties we investigate -- including
spin and concentration -- suggesting that baryonic processes and feedback
physics are instead critical in setting the scatter in the galaxy-halo size
relation. Given the relatively small scatter and the weak dependence of the
galaxy-halo size relation on redshift and halo properties for these low-mass
central galaxies, we propose using galaxy sizes as an independent method from
stellar masses to infer halo masses.
