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 $\lambda$. 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 $g_{\mathrm{s}}\sim g_{\mathrm{YM}}^2\sim \lambda /N$ and string tension $T\sim \sqrt{\lambda }$. Keeping only the leading in $1/T$ term at each order in $g_{\mathrm{s}}$ we observe that while the expansion of $⟨\mathcal{W}⟩$ 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 $⟨\mathcal{W}⟩$ 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 $⟨\mathcal{W}{\mathcal{O}}_J⟩$ 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.

43 pages, 1 figure. v3: minor changes

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• A dispersion relation for defect CFT
• Multipoint correlators on the supersymmetric Wilson line defect CFT
• Modular-invariant large-$N$ completion of an integrated correlator in $\mathcal{N}=4$ supersymmetric Yang-Mills theory
• Three-point functions in a $\mathcal{N}=2$ superconformal gauge theory and their strong-coupling limit
• Non-planar corrections in orbifold/orientifold $\mathcal{N}=2$ superconformal theories from localization
• Defect correlators in a $\mathcal{N}=2$ SCFT at strong coupling
• On topological recursion for Wilson loops in $\mathcal{N}=4$ SYM at strong coupling
• Wilson loop correlators in $\mathcal{N}=2$ superconformal quivers
• Perturbative bootstrap of the Wilson-line defect CFT: Bulk-defect-defect correlators
• A proof of loop equations in 2d topological gravity
• BPS Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)$ "orientifold" gauge theory and weak-strong coupling interpolation
• Exact 1/N expansion of Wilson loop correlators in $\mathcal{N}=4$ Super-Yang-Mills theory
• Loop equations for generalised eigenvalue models
• 't Hooft expansion of multi-boundary correlators in 2D topological gravity
• Two-Point Correlator of Chiral Primary Operators with a Wilson Line Defect in $\mathcal{N}=4$ SYM