  We obtain the effective action of tunnel-coupled quantum dots, by modeling
the system as a Luttinger liquid with multiple barriers. For a double dot
system, we find that the resonance conditions for perfect conductance form a
hexagon in the plane of the two gate voltages controlling the density of
electrons in each dot. We also explicitly obtain the functional dependence of
the interaction energy and peak-splitting on the gate voltage controlling
tunneling between the dots and their charging energies. Our results are in good
agreement with recent experimental results, from which we obtain the Luttinger
interaction parameter $K=0.74$.
