Octagons I: Combinatorics and Non-Planar Resummations

Understand

We explain how the 't Hooft expansion of correlators of half-BPS operators can be resummed in a large-charge limit in N=4 super Yang-Mills theory.

• The full correlator in the limit is given by a non-trivial function of two variables: One variable is the charge of the BPS operators divided by the square root of the number Nc of colors; the other variable is the octagon that contains all the 't Hooft coupling and spacetime dependence.
• At each genus g in the large Nc expansion, this function is a polynomial of degree 2g+2 in the octagon.
• We find several dual matrix model representations of the correlators in the large-charge limit.