o 1 2 3 4 t$_{o}$ t 2 E (k ) ||  x k$_{x}$ B$_{1}$ A$_{1}$ A$_{2}$ B FIG. 1: On the l.h.s. of the figure is picture a four leg ladder with equal hopping along and between the legs of the ladder. On the r.h.s are pictured the corresponding four bands, A$_{1}$$_{,}$$_{2}$ , B$_{1}$$_{,}$$_{2}$ of such a ladder. where c$_{n}$ is the corresponding annihilation operator of an electron on the n-th leg of the ladder. Close to half filling the Fermi velocities of the outer band pair labeled by B are smaller than those of the inner bands labeled by A , so that in the presence of interactions the effective dimensionless coupling constants for electrons in the inner bands are smaller than those for the outer bands. In the weak coupling limit, i.e. an onsite interaction characterized by U ≪ t , this Fermi velocity difference leads to a large difference in the characteristic energy scales and to a decoupling of the RG flows of the two band pairs. The outer band pair has the larger critical energy scale and flows to strong coupling first as the energy scale is lowered. 21–23 The inner band pair has a lower critical scale. Therefore in the first approximation one can treat inner and outer bands of individual 4-leg ladders as decoupled from each other. Then each band pair will effectively constitute a two-leg ladder. It is well known that two-leg ladders acquire spectral gaps for quite general interaction patterns. For the inner bands the smaller dimensionless couplings lead to smaller spectral gaps. At half filling each band pair is exactly half filled and behaves as a half filled 2-leg Hubbard ladder. The difference in the energy scales leads to a finite doping range x < x$_{c}$ where all the doped holes enter the inner band pair and the outer band pair remains exactly half filled. We note in passing that similar behavior is found also in the strong coupling limit, U ≫ t . 24 Given that a 4-leg ladder can be reduced to two 2-leg ladders, we will now recall some basic facts about 2-leg ladders. For general interactions they become either Luttinger liquids or dynamically generate spectral gaps. In the latter case an increased symmetry appears 4