  We report on a new mode of self-propulsion exhibited by compact drops of
active liquids on a substrate which, remarkably, is tractionless, i.e., which
imparts no mechanical stress locally on the surface. We show, both analytically
and by numerical simulation, that the equations of motion for an active nematic
drop possess a simple self-propelling solution, with no traction on the solid
surface and in which the direction of motion is controlled by the winding of
the nematic director field across the drop height. The physics underlying this
mode of motion has the same origins as that giving rise to the zero viscosity
observed in bacterial suspensions. This topologically protected tractionless
self-propusion provides a robust physical mechanism for efficient cell
migration in crowded environments like tissues.
