  Many previous Sum-of-Squares (SOS) lower bounds for CSPs had two deficiencies
related to global constraints. First, they were not able to support a
"cardinality constraint", as in, say, the Min-Bisection problem. Second, while
the pseudoexpectation of the objective function was shown to have some value
$\beta$, it did not necessarily actually "satisfy" the constraint "objective =
$\beta$". In this paper we show how to remedy both deficiencies in the case of
random CSPs, by translating \emph{global} constraints into \emph{local}
constraints. Using these ideas, we also show that degree-$\Omega(\sqrt{n})$ SOS
does not provide a $(\frac{4}{3} - \epsilon)$-approximation for Min-Bisection,
and degree-$\Omega(n)$ SOS does not provide a $(\frac{11}{12} +
\epsilon)$-approximation for Max-Bisection or a $(\frac{5}{4} -
\epsilon)$-approximation for Min-Bisection. No prior SOS lower bounds for these
problems were known.
