Handling Handles. Part II. Stratification and Data Analysis

Abstract

In a previous work, we proposed an integrability setup for computing non-planar corrections to correlation functions in $\mathcal{N}=4$ super Yang-Mills theory at any value of the coupling constant. The procedure consists of drawing all possible tree-level graphs on a Riemann surface of given genus, completing each graph to a triangulation, inserting a hexagon form factor into each face, and summing over a complete set of states on each edge of the triangulation. The summation over graphs can be interpreted as a quantization of the string moduli space integration. The quantization requires a careful treatment of the moduli space boundaries, which is realized by subtracting degenerate Riemann surfaces; this procedure is called stratification. In this work, we precisely formulate our proposal and perform several perturbative checks. These checks require hitherto unknown multi-particle mirror contributions at one loop, which we also compute.

arXiv comment99 pages, 261 figures, comments welcome; v2: minor improvements, updated references (published version)

References in corpus (41)

• Matrix String Theory
• Four-dimensional wall-crossing via three-dimensional field theory
• The su(2|2) Dynamic S-Matrix
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Quantum spectral curve for AdS_5/CFT_4
• Tailoring Three-Point Functions and Integrability
• Hexagonalization of Correlation Functions
• Leading singularities and off-shell conformal integrals
• Correlation Functions and Massive Kaluza-Klein Modes in the AdS/CFT Correspondence
• Tessellating cushions: four-point functions in N=4 SYM
• The S-matrix of String Bound States
• Extremal correlators in four-dimensional SCFT
• Tailoring Three-Point Functions and Integrability III. Classical Tunneling
• Quantum Spectral Curve and Structure Constants in N=4 SYM: Cusps in the Ladder Limit
• Tailoring Three-Point Functions and Integrability II. Weak/strong coupling match
• Explicit construction of nilpotent covariants in N=4 SYM
• Colour-dressed hexagon tessellations for correlation functions and non-planar corrections
• From Free Fields to AdS -- II
• On a Large N Degeneracy in N=4 SYM and the AdS/CFT Correspondence
• Quantum Integrability for Three-Point Functions
• The Bound State S-Matrix for AdS5 x S5 Superstring
• Extremal and next-to-extremal n-point correlators in four-dimensional SCFT
• Scattering Amplitudes -- Wilson Loops Duality for the First Non-planar Correction
• Hexagonalization of Correlation Functions II: Two-Particle Contributions
• Three-point functions in the SU(2) sector at strong coupling
• The structure of n-point functions of chiral primary operators in N=4 super Yang-Mills at one-loop
• On the worldsheet theories of strings dual to free large N gauge theories
• Four-point correlators of BPS operators in N=4 SYM at order g^4
• Wave functions and correlation functions for GKP strings from integrability
• Free Field Theory as a String Theory?
• Exact Correlators on the Wilson Loop in $\mathcal{N}=4$ SYM: Localization, Defect CFT, and Integrability
• Three-Point Functions and su(1|1) Spin Chains
• Matrix Theory Interpretation of DLCQ String Worldsheets
• On a worldsheet dual of the Gaussian matrix model
• Fermionic Correlators from Integrability
• Revisiting instanton corrections to the Konishi multiplet
• Matrix Model for Discretized Moduli Space
• Instanton effects in correlation functions on the light-cone
• Instanton corrections to twist-two operators
• On instanton effects in the operator product expansion
• Nodes as Composite Operators in Matrix Models

Cited by in corpus (29)

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• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• More Exact Results in the Wilson Loop Defect CFT: Bulk-Defect OPE, Nonplanar Corrections and Quantum Spectral Curve
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Octagons I: Combinatorics and Non-Planar Resummations
• Integrable S matrix, mirror TBA and spectrum for the stringy ${\text{AdS}}_3\times {\text{S}}^3\times {\text{S}}^3\times {\text{S}}^1$ WZW model
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• The Octagon as a Determinant
• Non-planar form factors of generic local operators via on-shell unitarity and color-kinematics duality
• Hexagons and Correlators in the Fishnet Theory
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Non-planar data of $\mathcal{N}=4$ SYM
• Colour-Twist Operators I: Spectrum and Wave Functions
• Decagon at Two Loops
• Functional Equations and Separation of Variables for Exact g-Function
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Non-planar cusp and transcendental anomalous dimension at four loops in N=4 supersymmetric Yang-Mills theory
• Dynamical Spin Chains in 4D $\mathcal{N}=2$ SCFTs
• On structure constants with two spinning twist-two operators
• Three-point functions at strong coupling in the BMN limit
• Octagon with finite bridge: free fermions and determinant identities
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• Higher-Point Correlators in N=4 SYM: Generating Functions
• Three-Point Functions in ABJM and Bethe Ansatz
• Multi-trace Correlators from Permutations as Moduli Space
• Orthogonality of Q-Functions up to Wrapping in Planar N=4 Super Yang-Mills Theory
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons