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 $$ \mathcal{W} $$ W in $$ \mathcal{N} $$ 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 $$ {g}_{\mathrm{s}}\sim {g}_{\mathrm{YM}}^2\sim \lambda /N $$ g s ∼ g YM 2 ∼ λ / N and string tension $$ T\sim \sqrt{\lambda } $$ T ∼ λ . Keeping only the leading in 1/T term at each order in gs we observe that while the expansion of $$ \left\langle \mathcal{W}\right\rangle $$ W is a series in $$ {g}_{\mathrm{s}}^2/T $$ g s 2 / T , the correlator of the Wilson loop with chiral primary operators $$ {\mathcal{O}}_J $$ O J has expansion in powers of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Like in the case of $$ \left\langle \mathcal{W}\right\rangle $$ W where these leading terms are known to resum into an exponential of a “one-handle” contribution $$ \sim {g}_{\mathrm{s}}^2/T $$ ∼ g s 2 / T , the leading strong coupling terms in $$ \left\langle {\mathcal{WO}}_J\right\rangle $$ WO J sum up to a simple square root function of $$ {g}_{\mathrm{s}}^2/{T}^2 $$ g s 2 / T 2 . Analogous expansions in powers of $$ {g}_{\mathrm{s}}^2/T $$ 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.