  Synthetic fields applied to ultracold quantum gases can realize topological
phases that transcend conventional Bose and Fermi-liquid paradigms. Raman laser
beams in particular are under scrutiny as a route to create synthetic fields in
neutral gases to mimic ordinary magnetic and electric fields acting on charged
matter. Yet external laser beams can impose heating and losses that make
cooling into many-body topological phases challenging. We propose that atomic
or molecular dipoles placed in optical lattices can realize a topological phase
without synthetic fields by placing them in certain frustrated lattices. We use
numerical modeling on a specific example to show that the interactions between
dipolar fermions placed in a kagome optical lattice spontaneously break time
reversal symmetry to lead to a topological Mott insulator, a chiral topological
phase generated entirely by interactions. We estimate realistic entropy and
trapping parameters to argue that this intriguing phase of matter can be probed
with quantum gases using a combination of recently implemented technologies.
