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

A bstract Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop W W in N 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 g s ∼ g YM 2 ∼ λ / N and string tension T~ √λ T ∼ λ . Keeping only the leading in 1/ T term at each order in g s we observe that while the expansion of W W is a series in gₛ²/T g s 2 / T , the correlator of the Wilson loop with chiral primary operators OJ O J has expansion in powers of gₛ²/T² g s 2 / T 2 . Like in the case of W W where these leading terms are known to resum into an exponential of a “one-handle” contribution ~ gₛ²/T ∼ g s 2 / T , the leading strong coupling terms in WOJ WO J sum up to a simple square root function of gₛ²/T² g s 2 / T 2 . Analogous expansions in powers of gₛ²/T g s 2 / 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.