Interacting Emergent Yang-Mills theory

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.Comment: 27 pages + 3 pages of appendices, 4 figures. v4: misprint correcte