  We give a new twist to an old-fashioned topic in quantum field theory
describing violations of the chiral charge conservation of massless fermions
through Adler-Bell-Jackiw anomalies in the background of instanton fields in
the context of non-relativistic Lifshitz theories. The results we report here
summarize in a nut-shell our earlier work on the subject found in
arXiv:1103.5693 and arXiv:1110.1332. We present simple examples where index
computations can be carried out explicitly focusing, in particular, to
gravitational models of Lifshitz type and highlight their differences from
ordinary gravity in four space-time dimensions.
