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

Abstract

Starting with some known localization (matrix model) representations for correlators involving 1/2 BPS circular Wilson loop mathcal{W} in mathcal{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 {g}_{mathrm{s}}sim {g}_{mathrm{YM}}^2sim lambda /N and string tension Tsim sqrt{lambda } . Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of leftlangle mathcal{W}rightrangle is a series in {g}_{mathrm{s}}^2/T , the correlator of the Wilson loop with chiral primary operators {mathcal{O}}_J has expansion in powers of {g}_{mathrm{s}}^2/{T}^2 . Like in the case of leftlangle mathcal{W}rightrangle where these leading terms are known to resum into an exponential of a “one-handle” contribution sim {g}_{mathrm{s}}^2/T , the leading strong coupling terms in leftlangle {mathcal{WO}}_Jrightrangle sum up to a simple square root function of {g}_{mathrm{s}}^2/{T}^2 . Analogous expansions in powers of {g}_{mathrm{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.