Environmental Evidence for Overly Massive Black Holes in Low Mass Galaxies and a Black Hole - Halo Mass Relation at $z \sim 5$

JWST observations have unveiled faint active galactic nuclei (AGN) at high-redshift that provide insights on the formation of supermassive black holes (SMBHs) and their coevolution with galaxies. However, disentangling stellar from AGN light in these sources is challenging. Here, we use an empirical approach to infer the average stellar mass of 6 faint broad line (BL) Halpha emitters at z = 4 - 5 with BH masses ~ 6 (4 - 15)x10^6 Msun, with a method independent of their spectral energy distribution (SED). We use the deep JWST/NIRcam grism survey ALT to measure the over-densities around BL-Halpha emitters and around a spectroscopic reference sample of ~300 galaxies. In our reference sample, we find that Mpc-scale over-density correlates with stellar mass, while pair counts are flat below ~50 kpc due to satellites. Their large-scale environments suggest that BL-Halpha emitters are hosted by galaxies with stellar masses ~5x10^7 Msun, ~40 times lower than those inferred from galaxy-only SED fits. Adding measurements around more luminous z~6 AGNs, we find tentative correlations between line width, BH mass and the over-density, suggestive of a steep BH to halo mass relation. The main implications are (1) when BH masses are taken at face value, we confirm extremely high BH to stellar mass ratios of ~10 %, (2) the low stellar mass galaxies hosting growing SMBHs are in tension with typical hydrodynamical simulations, except those without feedback, (3) a 1 % duty cycle implied by the host mass hints at super-Eddington accretion, which may imply over-estimated SMBH masses, (4) the masses are at odds with a high stellar density interpretation of the line broadening, (5) our results imply a diversity of galaxy masses, environments and SEDs among AGN samples, depending on their luminosity.