The rare top decay t-> c l+l-, which involves flavor violation, is studied as
a possible probe of new physics. This decay is analyzed with the simplest
Standard Model extensions with additional gauge symmetry formalism. The
considered extension is the Left-Right Symmetric Model, including a new neutral
gauge boson Z' that allows to obtain the decay at tree level through Flavor
Changing Neutral Currents (FCNC) couplings. The neutral gauge boson couplings
are considered diagonal but family non-universal in order to induce these FCNC.
We find the $BR(t-> c l+l-)~10^{-13} for a range 1 TeV < M_{Z'} < 3 TeV.Comment: 9 pages, 6 figure