On the structure of non-planar strong coupling corrections to correlators of BPS Wilson loops and chiral primary operators

Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop W in N = 4 SYM theory we work out their 1/N expansions in the limit of large ’t Hooft coupling λ. Motivated by a possibility of eventual matching to higher genus corrections in dual string theory we follow arXiv:2007.08512 and express the result in terms of the string coupling gs∼gYM2∼λ/N and string tension T∼λ. Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of 〈 W〉 is a series in gs2/T, the correlator of the Wilson loop with chiral primary operators OJ has expansion in powers of gs2/T2. Like in the case of 〈 W〉 where these leading terms are known to resum into an exponential of a “one-handle” contribution ∼gs2/T, the leading strong coupling terms in 〈 WOJ〉 sum up to a simple square root function of gs2/T2. Analogous expansions in powers of gs2/T are found for correlators of several coincident Wilson loops and they again have a simple resummed form. We also find similar expansions for correlators of coincident 1/2 BPS Wilson loops in the ABJM theory.