  We explore the galaxy structure of four tidal disruption event (TDE) host
galaxies on 30 pc to kpc scales using HST WFC3 multi-band imaging. The star
formation histories of these hosts are diverse, including one post-starburst
galaxy (ASASSN-14li), two hosts with recent weak starbursts (ASASSN-14ae and
iPTF15af), and one early type (PTF09ge). Compared to early type galaxies of
similar stellar masses, the TDE hosts have higher central surface brightnesses
and stellar mass surface densities on 30-100 pc scales. The TDE hosts do not
show the large, kpc-scale tidal disruptions seen in some post-starburst
galaxies; the hosts have low morphological asymmetries similar to those of
early type galaxies. The lack of strong asymmetries are inconsistent with a
recent major (~1:1 mass) merger, although minor ($\lesssim$1:3) mergers are
possible. Given the time elapsed since the end of the starbursts in the three
post-burst TDE hosts and the constraints on the merger mass ratios, it is
unlikely that a bound supermassive black hole binary (SMBHB) has had time to
coalesce. The TDE hosts have low central (<140 pc) ellipticities compared to
early type galaxies. The low central ellipticities disfavor a strong radial
anisotropy as the cause for the enhanced TDE rate, although we cannot rule out
eccentric disks at the scale of the black hole gravitational radius of
influence (~1 pc). These observations suggest that the high central stellar
densities are a more important driver than SMBHBs or radial anisotropies in
increasing the TDE rate in galaxies with recent starbursts.
