  New physics in the rare top decays $t \to q \ell^+\ell^-$ is currently very
weakly constrained. We show that in a large class of Standard Model extensions,
existing experimental constraints on new physics in flavor-conserving processes
imply strong indirect bounds on new physics contributions to flavor-violating
processes of the form $t \to q \ell^+\ell^-$. These indirect bounds arise from
basic principles of quantum field theory together with a few generic conditions
on the UV structure of the theory, and are roughly an order of magnitude
stronger than the present experimental bounds on the same processes. These
constraints provide a theoretically motivated target for experimental searches
for $t \to q \ell^+\ell^-$: violation of these bounds would exclude a large
class of new physics models, and would provide nontrivial insight into the UV
behavior of the new physics.
