  We consider a RG approach for the plasma of magnetic monopoles of the
Ioffe-Larkin approach to the t-J model. We first derive the interaction
parameters of the 2+1 plasma of magnetic monopoles. The total charge along the
time axis is constrained to be zero for each lattice plaquette. Under the
one-plaquette approximation, the problem is equivalent to a one dimensional
neutral plasma interacting via a potential $V(t) \sim t^{\alpha}$, with
$\alpha=1/3$. The plasma is in a dipolar phase if $\alpha \ge 1$ and a
possibility of transition towards a Debye screening phase arises if $\alpha <
1$, so that there exists a critical Fermi wave vector $k_f^{*}$ such as the
plasma is Debye screening if $k_f<k_f^{*}$ and confined if $k_f>k_f^{*}$. The
2+1 dimensional problem is treated numerically. We show that $k_f^{*}$
decreases and goes to zero as the number of colors increases. This suggests
that the assumption of spin-charge decoupling within the slave-boson scheme is
self-consistent at large enough values of $N$ and small enough doping.
Elsewhere, a confining force between spinons and antiholons appears, suggesting
a transition to a Fermi liquid state.
