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.

arXiv comment43 pages, 1 figure. v3: minor changes

References in corpus (69)

• The Large N Limit of Superconformal Field Theories and Supergravity
• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Wilson loops in large N field theories
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Wilson Loops in N=4 Supersymmetric Yang--Mills Theory
• An Exact Prediction of N=4 SUSYM Theory for String Theory
• Wilson Loops and Minimal Surfaces
• From weak to strong coupling in ABJM theory
• All genus correlation functions for the hermitian 1-matrix model
• The Operator Product Expansion for Wilson Loops and Surfaces in the Large N Limit
• Aspects of Large N Gauge Theory Dynamics as Seen by String Theory
• Chern-Simons theory, matrix integrals, and perturbative three-manifold invariants
• A New Double-Scaling Limit of N=4 Super Yang-Mills Theory and PP-Wave Strings
• Integrability and Matrix Models
• All-genus calculation of Wilson loops using D-branes
• Green-Schwarz String in AdS_5 x S^5: Semiclassical Partition Function
• Matrix Model as a Mirror of Chern-Simons Theory
• Exact Results in ABJM Theory from Topological Strings
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Higher genus correlators for the hermitian matrix model with multiple cuts
• Supersymmetric Wilson loops on S^3
• Correlation Functions of Coulomb Branch Operators
• Supersymmetric Wilson loops
• Higher rank Wilson loops from a matrix model
• 1/4 BPS circular loops, unstable world-sheet instantons and the matrix model
• Correlators of local operators and 1/8 BPS Wilson loops on S^2 from 2d YM and matrix models
• More supersymmetric Wilson loops
• Wilson Loops in N=4 SYM and Fermion Droplets
• Wilson loops: From four-dimensional SYM to two-dimensional YM
• Wilson Loop Correlator in the AdS/CFT Correspondence
• More exact predictions of SUSYM for string theory
• Correlators of Wilson loops and local operators from multi-matrix models and strings in AdS
• Wilson loop correlators at strong coupling: from matrices to bubbling geometries
• Two-point Correlators in N=2 Gauge Theories
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• The Spectral Curve of the Lens Space Matrix Model
• Notes on supersymmetric Wilson loops on a two-sphere
• Correlators between Wilson loop and chiral operators in N=2 conformal gauge theories
• Open string fluctuations in AdS_5xS^5 and operators with large R-charge
• Correlators of supersymmetric Wilson-loops, protected operators and matrix models in N=4 SYM
• Single Particle Operators and their Correlators in Free $\mathcal{N}=4$ SYM
• Operator product expansion of higher rank Wilson loops from D-branes and matrix models
• Localization and AdS/CFT Correspondence
• Matrix Models vs. Matrix Integrals
• Wilson Loops in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory from Random Matrix Theory
• Wilson Loops and Chiral Correlators on Squashed Sphere
• Comparing strings in AdS(5)xS(5) to planar diagrams: an example
• Exact 1/4 BPS Loop - Chiral Primary Correlator
• Correlators of supersymmetric Wilson loops at weak and strong coupling
• Strong coupling expansion of circular Wilson loops and string theories in AdS${}_5\times {\mathrm{S}}^5$ and AdS${}_4\times {\mathrm{CP}}^3$
• Exact 2-point function in Hermitian matrix model
• Limiting Geometries of Two Circular Maldacena-Wilson Loop Operators
• Connected correlator of 1/2 BPS Wilson loops in $\mathcal{N}=4$ SYM
• Correlation function of circular Wilson loop with two local operators and conformal invariance
• Correlators of chiral primaries and 1/8 BPS Wilson loops from perturbation theory
• Boundary condition for D-brane from Wilson loop, and gravitational interpretation of eigenvalue in matrix model in AdS/CFT correspondence
• On strong-coupling correlation functions of circular Wilson loops and local operators
• Strings in Bubbling Geometries and Dual Wilson Loop Correlators
• Two-Loop Spectroscopy of Short ABJM Operators
• Dyson equations for correlators of Wilson loops
• Ladder Limit for Correlators of Wilson Loops
• 't Hooft Expansion of 1/2 BPS Wilson Loop
• Antisymmetric Wilson loops in N = 4 SYM: from exact results to non-planar corrections
• Note on generating functions and connected correlators of 1/2-BPS Wilson loops in $\mathcal{N}=4$ SYM theory
• Exact results for Wilson loops in orbifold ABJM theory
• Combinatorics of Wilson loops in $\mathcal{N}=4$ SYM theory
• On Wilson loops for two touching circles with opposite orientation
• Wilson loop and its correlators in the limit of large coupling constant

Cited by in corpus (18)

• Bootstrapping holographic defect correlators in $\mathcal{N}=4$ super Yang-Mills
• $1/N$ expansion of circular Wilson loop in $\mathcal{N}=2$ superconformal $SU(N)\times SU(N)$ quiver
• Wilson loops at large $N$ and the quantum M2 brane
• 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