Lorentz Anomalies

Associated with the local Lorentz symmetry of gravitational interactions of fermions there are chiral anomalies in ($4n+2$)-dimensional space-times. We present chiral Lorentz anomalies in two and six dimensions. Existence of chiral Lorentz anomalies implies that quantum effects induce a breakdown of local Lorentz symmetry in $4n+2$ dimensions, in general, in theories containing chiral Weyl fermions.