  Antisymmetric tensor fields interacting with quarks and leptons have been
proposed as a possible solution to the gauge hierarchy problem. We compute the
one-loop beta function for a quartic self-interaction of the chiral
antisymmetric tensor fields. Fluctuations of the top quark drive the
corresponding running coupling to a negative value as the renormalization scale
is lowered. This may indicate a non-vanishing expectation value of the tensor
field, and thus a spontaneous breaking of Lorentz invariance. Settling this
issue will need the inclusion of tensor loops.
