On thing to keep in mind is that IR and UV divergences appear in different kinematical regimes: UV divergences are basically due to the fact that in loop integrals there are not sufficient propagators to make the integral fall off at infinity. E.g for a bubble integral

$\int d^4l \frac{1}{l^2(l-p)^2}$ will be logarithmically divergent. Do for instance a Taylor expansion of this expression for the loop momentum becoming large then this becomes obvious.

IR divergences however live in a completely different regime: they appear either when two particles becoming collinear $p_1\sim p_2$ or because some particles become soft $p_i\sim0$.

Or put a little more condensed:

UV: loop momentum becomes large

IR: external momenta become collinear/soft.

This is one way to see why these two kinds of divergence are not connected. Nima and company propably meant just this but in fancier terms.

This post imported from StackExchange Physics at 2014-04-15 16:45 (UCT), posted by SE-user A friendly helper