  In this article, subleading (in $1/N$) corrections to the action of the one
loop dilatation operator in the su(3) sector of $\mathcal{N}=4$ super
Yang-Mills theory are studied. We focus on the system of operators dual to two
giant graviton systems, which have a bare dimension $\sim\mathcal{O}(N)$ and
are a linear combination of restricted Schur polynomials with $p=2$ long
columns. At the leading order the dilatation operator gives rise to the free
part of an emergent Yang-Mills theory, arising from the open string excitations
of the giant gravitons. We verify that the terms we study describe interactions
between these open string excitations. The interactions have the
U(1)$\times$U(1) gauge invariance expected for a pair of separated branes.
