  We construct and discuss the field theory for tensorial nematic order
parameter coupled to gapless four-component fermions at the quadratic band
touching point in three (spatial) dimensions. Within a properly formulated
epsilon-expansion this theory is found to have a quantum critical point, which
describes the (presumably continuous) transition from the semimetal into a
(nematic) Mott insulator. The latter phase breaks the rotational, but not the
time-reversal symmetry, and may be relevant to materials such as gray tin or
mercury telluride at low temperatures. The critical point represents a simple
quantum analogue of the familiar classical isotropic-to-nematic transition in
liquid crystals. The properties and the consequences of this quantum critical
point are discussed. Its existence supports the scenario of the "fixed-point
collision", according to which three-dimensional Fermi systems with quadratic
band touching and long-range Coulomb interactions are unstable towards the
gapped nematic ground state at low temperatures.
