Hexagonalization of Correlation Functions II: Two-Particle Contributions

Abstract

In this work, we compute one-loop planar five-point functions in $\mathcal{N}$=4 super-Yang-Mills using integrability. As in the previous work, we decompose the correlation functions into hexagon form factors and glue them using the weight factors which depend on the cross ratios. The main new ingredient in the computation, as compared to the four-point functions studied in the previous paper, is the two-particle mirror contribution. We develop techniques to evaluate it and find agreement with the perturbative results in all the cases we analyzed. In addition, we consider next-to-extremal four-point functions, which are known to be protected, and show that the sum of one-particle and two-particle contributions at one loop adds up to zero as expected. The tools developed in this work would be useful for computing higher-particle contributions which would be relevant for more complicated quantities such as higher-loop corrections and non-planar correlators.

36 pages

References in corpus (8)

• Four-loop perturbative Konishi from strings and finite size effects for multiparticle states
• Hexagonalization of Correlation Functions
• The S-matrix of String Bound States
• The Classical r-matrix of AdS/CFT and its Lie Bialgebra Structure
• Bound States, Yangian Symmetry and Classical r-matrix for the AdS5 x S5 Superstring
• On the Scattering of Magnon Boundstates
• Fermionic Correlators from Integrability
• The Bethe Ansatz for AdS5 x S5 Bound States

Cited by in corpus (38)

• Bootstrapping the simplest correlator in planar N = 4 SYM at all loops
• Handling Handles: Nonplanar Integrability in $\mathcal{N}=4$ Supersymmetric Yang-Mills Theory
• Perturbative Four-Point Functions In Planar N=4 SYM From Hexagonalization
• Determinant formula for the octagon form factor in $\mathcal{N}$=4 SYM
• Ten dimensional symmetry of N=4 SYM correlators
• Exactly solvable magnet of conformal spins in four dimensions
• 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
• Handling Handles. Part II. Stratification and Data Analysis
• The Octagon as a Determinant
• Open-closed Hyperbolic String Vertices
• The SAGEX Review on Scattering Amplitudes, Chapter 8: Half BPS correlators
• All five-loop planar four-point functions of half-BPS operators in $\mathcal{N}=4$ SYM
• Exactly solvable single-trace four point correlators in $\chi$CFT${}_4$
• Correlation Functions on the Half-BPS Wilson Loop: Perturbation and Hexagonalization
• Hexagons and Correlators in the Fishnet Theory
• Positivity of hexagon perturbation theory
• Decagon at Two Loops
• Infrared properties of five-point massive amplitudes in N=4 SYM on the Coulomb branch
• Integrable bootstrap for AdS3/CFT2 correlation functions
• Higher-Point Integrands in N=4 super Yang-Mills Theory
• Hexagonalization of Fishnet integrals I: mirror excitations
• On structure constants with two spinning twist-two operators
• Octagon with finite bridge: free fermions and determinant identities
• Three-point functions at strong coupling in the BMN limit
• Pentagon OPE resummation in N=4 SYM: hexagons with one effective particle contribution
• Stampedes II: Null Polygons in Conformal Gauge Theory
• Light-cone limits of large rectangular fishnets
• ABJM quantum spectral curve at twist 1: algorithmic perturbative solution
• Fishnet four-point integrals: integrable representations and thermodynamic limits
• Cutting the cylinder into squares: The square form factor
• Three-point Functions in $\mathcal{N}=4$ SYM at Finite $N_c$ and Background Independence
• On analytical perturbative solution of ABJM quantum spectral curve
• Polylogarithms from the bound state S-matrix
• Three-Point Functions in ABJM and Bethe Ansatz
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• Bound State Scattering Simplified
• Higher-Point Correlators in N=4 SYM: Ten-Dimensional Null Polygons