  We present the first ab initio calculations of neutrinoless double beta decay
matrix elements in $A=6$-$12$ nuclei using Variational Monte Carlo wave
functions obtained from the Argonne $v_{18}$ two-nucleon potential and
Illinois-7 three-nucleon interaction. We study both light Majorana neutrino
exchange and potentials arising from a large class of multi-TeV mechanisms of
lepton number violation. Our results provide benchmarks to be used in testing
many-body methods that can be extended to the heavy nuclei of experimental
interest. In light nuclei we have also studied the impact of two-body short
range correlations and the use of different forms for the transition operators,
such as those corresponding to different orders in chiral effective theory.
