The Four-Loop Planar Amplitude and Cusp Anomalous Dimension in Maximally Supersymmetric Yang-Mills Theory

Abstract

We present an expression for the leading-color (planar) four-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4-2 e dimensions, in terms of eight separate integrals. The expression is based on consistency of unitarity cuts and infrared divergences. We expand the integrals around e=0, and obtain analytic expressions for the poles from 1/e^8 through 1/e^4. We give numerical results for the coefficients of the 1/e^3 and 1/e^2 poles. These results all match the known exponentiated structure of the infrared divergences, at four separate kinematic points. The value of the 1/e^2 coefficient allows us to test a conjecture of Eden and Staudacher for the four-loop cusp (soft) anomalous dimension. We find that the conjecture is incorrect, although our numerical results suggest that a simple modification of the expression, flipping the sign of the term containing zeta_3^2, may yield the correct answer. Our numerical value can be used, in a scheme proposed by Kotikov, Lipatov and Velizhanin, to estimate the two constants in the strong-coupling expansion of the cusp anomalous dimension that are known from string theory. The estimate works to 2.6% and 5% accuracy, providing non-trivial evidence in support of the AdS/CFT correspondence. We also use the known constants in the strong-coupling expansion as additional input to provide approximations to the cusp anomalous dimension which should be accurate to under one percent for all values of the coupling. When the evaluations of the integrals are completed through the finite terms, it will be possible to test the iterative, exponentiated structure of the finite terms in the four-loop four-point amplitude, which was uncovered earlier at two and three loops.

72 pages, 15 figures, v2 minor corrections

References in corpus (111)

• Gauge Theory Correlators from Non-Critical String Theory
• The Large N Limit of Superconformal Field Theories and Supergravity
• Large N Field Theories, String Theory and Gravity
• Strings in flat space and pp waves from $\mathcal{N}=4$ Super Yang Mills
• The Bethe-Ansatz for N=4 Super Yang-Mills
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• The Three-Loop Splitting Functions in QCD: The Non-Singlet Case
• Harmonic Polylogarithms
• Fusing Gauge Theory Tree Amplitudes Into Loop Amplitudes
• Differential Equations for Two-Loop Four-Point Functions
• Cuba - a library for multidimensional numerical integration
• Hidden Symmetries of the AdS_5 x S^5 Superstring
• A semi-classical limit of the gauge/string correspondence
• The Three-Loop Splitting Functions in QCD: The Singlet Case
• Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
• The Singular Behaviour of QCD Amplitudes at Two-loop Order
• The N=4 SYM Integrable Super Spin Chain
• The Dilatation Operator of Conformal N=4 Super Yang-Mills Theory
• JaxoDraw: A graphical user interface for drawing Feynman diagrams
• Long-Range PSU(2,2|4) Bethe Ansaetze for Gauge Theory and Strings
• Semiclassical quantization of rotating superstring in AdS_5 x S^5
• Bethe Ansatz for Quantum Strings
• Magic identities for conformal four-point integrals
• The Complete One-Loop Dilatation Operator of N=4 Super Yang-Mills Theory
• Numerical evaluation of multiple polylogarithms
• On the Relationship between Yang-Mills Theory and Gravity and its Implication for Ultraviolet Divergences
• Three-loop universal anomalous dimension of the Wilson operators in N=4 SUSY Yang-Mills model
• Automatized analytic continuation of Mellin-Barnes integrals
• HPL, a Mathematica implementation of the harmonic polylogarithms
• Multi-Leg One-Loop Gravity Amplitudes from Gauge Theory
• The Factorized S-Matrix of CFT/AdS
• The AdS_5xS^5 superstring worldsheet S-matrix and crossing symmetry
• Multi-loop Amplitudes and Resummation
• Analytical Result for Dimensionally Regularized Massless On-shell Double Box
• The su(2|3) Dynamic Spin Chain
• Non-planar massless two-loop Feynman diagrams with four on-shell legs
• Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory
• A Crossing-Symmetric Phase for AdS_5 x S^5 Strings
• Massive Loop Amplitudes from Unitarity
• Structure functions for large $x$ and renormalization of Wilson loops
• Nested Sums, Expansion of Transcendental Functions and Multi-Scale Multi-Loop Integrals
• Progress in One-Loop QCD Computations
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The planar topologies
• Two-Loop Four-Gluon Amplitudes in N=4 Super-Yang-Mills
• Baryon Distribution Amplitudes in QCD
• Numerical Evaluation of Harmonic Polylogarithms
• Quantum corrections to the string Bethe ansatz
• Two-Loop g -> gg Splitting Amplitudes in QCD
• Integrability of three-particle evolution equations in QCD
• A Relation Between Approaches to Integrability in Superconformal Yang-Mills Theory
• Matching Higher Conserved Charges for Strings and Spins
• Gauge-string duality for superconformal deformations of N=4 Super Yang-Mills theory
• Supersymmetric Regularization, Two-Loop QCD Amplitudes and Coupling Shifts
• Anomalous dimensions of Wilson operators in N=4 SYM theory
• Field Theory Tests for Correlators in the AdS/CFT Correspondence
• Gauge/string duality for QCD conformal operators
• Two-Loop Master Integrals for ${\gamma }^{\ast }\to 3$ Jets: The non-planar topologies
• Revisiting parton evolution and the large-x limit
• Quantum Consistency of the Superstring in AdS_5 x S^5 Background
• A note on twist two operators in N=4 SYM and Wilson loops in Minkowski signature
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• Logarithmic scaling in gauge/string correspondence
• Three-Loop Four-Point Correlator in N=4 SYM
• On Quantum Corrections to Spinning Strings and Bethe Equations
• Anomalous dimensions in N=4 SYM theory at order g^4
• Planar N=4 Gauge Theory and the Hubbard Model
• Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators
• Next-to-next-to-leading logarithmic threshold resummation for deep-inelastic scattering and the Drell-Yan process
• Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes
• Two-Loop Iteration of Five-Point N=4 Super-Yang-Mills Amplitudes
• The Operator Product Expansion of N=4 SYM and the 4-point Functions of Supergravity
• Four-point Functions of Lowest Weight CPOs in N=4 SYM_4 in Supergravity Approximation
• Fine structure of spectrum of twist-three operators in QCD
• Inherited Twistor-Space Structure of Gravity Loop Amplitudes
• The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
• The No-Triangle Hypothesis for N=8 Supergravity
• On the logarithmic behaviour in N=4 SYM theory
• Analytical Result for Dimensionally Regularized Massive On-Shell Planar Double Box
• Two-Loop Helicity Amplitudes for Quark-Quark Scattering in QCD and Gluino-Gluino Scattering in Supersymmetric Yang-Mills Theory
• 3-Point Functions in N=4 Yang-Mills
• Simplifications of four-point functions in N=4 supersymmetric Yang-Mills theory at two loops
• A Universality Test of the Quantum String Bethe Ansatz
• Stringy sums and corrections to the quantum string Bethe ansatz
• Dilatation operator in (super-)Yang-Mills theories on the light-cone
• Iterative Structure Within The Five-Particle Two-Loop Amplitude
• Analytical Evaluation of Dimensionally Regularized Massive On-Shell Double Boxes
• Exponentiation of the Drell-Yan cross section near partonic threshold in the DIS and MSbar schemes
• Two-point functions of chiral operators in {\cal N}=4 SYM at order g^4
• Light-Cone Wilson Loops and the String/Gauge Correspondence
• Non-Singlet Structure Functions at Three Loops: Fermionic Contributions
• Six-Point One-Loop N=8 Supergravity NMHV Amplitudes and their IR behaviour
• Higher loops, integrability and the near BMN limit
• Quantum integrability in (super) Yang-Mills theory on the light-cone
• Numerical evaluation of loop integrals
• Analytical Result for Dimensionally Regularized Massless On-Shell Planar Triple Box
• Non-protected operators in N=4 SYM and multiparticle states of AdS_5 SUGRA
• Analytical Result for Dimensionally Regularized Massless Master Double Box with One Leg off Shell
• Higher Orders in A(α_s)/[1-x]_+ of Non-Singlet Partonic Splitting Functions
• Non-renormalisation of extremal correlators in N=4 SYM theory
• Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell
• Non-renormalization of next-to-extremal correlators in N=4 SYM and the AdS/CFT correspondence
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• The planar four-point master integrals for massive two-loop Bhabha scattering
• Towards the exact dilatation operator of N=4 super Yang-Mills theory
• Cusped SYM Wilson loop at two loops and beyond
• Multigluon amplitudes, $\mathcal{N}=4$ constraints and the WZW model
• Unitarity-based Techniques for One-Loop Calculations in QCD
• On the Scattering Phase for AdS_5 x S^5 Strings
• Evaluating multiloop Feynman integrals by Mellin-Barnes representation
• Effective action of dressed mean fields for N = 4 super-Yang-Mills theory
• Perturbative Gravity and Twistor Space

Cited by in corpus (307)

• New Relations for Gauge-Theory Amplitudes
• Transcendentality and Crossing
• Conformal collider physics: Energy and charge correlations
• Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
• Conformal properties of four-gluon planar amplitudes and Wilson loops
• The Amplituhedron
• MHV Amplitudes in N=4 Super Yang-Mills and Wilson Loops
• On the Structure of Infrared Singularities of Gauge-Theory Amplitudes
• Infrared singularities of scattering amplitudes in perturbative QCD
• Conformal Ward identities for Wilson loops and a test of the duality with gluon amplitudes
• On planar gluon amplitudes/Wilson loops duality
• Foundations of the AdS_5 x S^5 Superstring. Part I
• Yangian symmetry of scattering amplitudes in N=4 super Yang-Mills theory
• Comments on gluon scattering amplitudes via AdS/CFT
• Hexagon Wilson loop = six-gluon MHV amplitude
• The Two-Loop Six-Gluon MHV Amplitude in Maximally Supersymmetric Yang-Mills Theory
• The Ultraviolet Behavior of N=8 Supergravity at Four Loops
• Bootstrapping the three-loop hexagon
• On-Shell Methods in Perturbative QCD
• Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops
• Motivic Amplitudes and Cluster Coordinates
• The Zamolodchikov-Faddeev Algebra for AdS_5 x S^5 Superstring
• Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability
• Simplifying Multiloop Integrands and Ultraviolet Divergences of Gauge Theory and Gravity Amplitudes
• Towards a Basis for Planar Two-Loop Integrals
• Scattering into the fifth dimension of N=4 super Yang-Mills
• Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity
• On String S-matrix, Bound States and TBA
• A supermatrix model for N=6 super Chern-Simons-matter theory
• Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory
• The all loop AdS4/CFT3 Bethe ansatz
• Bootstrapping an NMHV amplitude through three loops
• Scattering Amplitudes, Wilson Loops and the String/Gauge Theory Correspondence
• Cusp anomalous dimension in maximally supersymmetric Yang-Mills theory at strong coupling
• BFKL Pomeron, Reggeized gluons and Bern-Dixon-Smirnov amplitudes
• Into the Amplituhedron
• Superconformal symmetry and two-loop amplitudes in planar N=4 super Yang-Mills
• Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• On the Resolution of Singularities of Multiple Mellin-Barnes Integrals
• Heptagons from the Steinmann Cluster Bootstrap
• The S-Matrix in Twistor Space
• String hypothesis for the AdS_5 x S^5 mirror
• Supersymmetric Wilson loops on S^3
• A Test of the AdS/CFT Correspondence Using High-Spin Operators
• Four loop twist two, BFKL, wrapping and strings
• Extension of HPL to complex arguments
• A Two-Loop Five-Gluon Helicity Amplitude in QCD
• All tree-level amplitudes in N=4 SYM
• From correlation functions to scattering amplitudes
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• Two-loop world-sheet corrections in AdS_5 x S^5 superstring
• Six-Gluon Amplitudes in Planar $\mathcal{N}=4$ Super-Yang-Mills Theory at Six and Seven Loops
• Basics of Generalized Unitarity
• Hepta-Cuts of Two-Loop Scattering Amplitudes
• Hidden symmetry of four-point correlation functions and amplitudes in N=4 SYM
• Worldsheet Scattering in AdS_5 x S^5
• Constructing the correlation function of four stress-tensor multiplets and the four-particle amplitude in N=4 SYM
• Wrapping interactions at strong coupling -- the giant magnon
• Logarithmic corrections to higher twist scaling at strong coupling from AdS/CFT
• Scattering Amplitudes from Multivariate Polynomial Division
• On the Integrand-Reduction Method for Two-Loop Scattering Amplitudes
• Maximal Unitarity at Two Loops
• N >= 4 Supergravity Amplitudes from Gauge Theory at Two Loops
• Exacting N=4 Superconformal Symmetry
• Bootstrapping the QCD soft anomalous dimension
• Positive Amplitudes In The Amplituhedron
• The Cosmic Galois Group and Extended Steinmann Relations for Planar $\mathcal{N}=4$ SYM Amplitudes
• Single soft gluon emission at two loops
• Connecting giant magnons to the pp-wave: An interpolating limit of $Ad{S}_5\times S^5$
• Four-Loop Cusp Anomalous Dimension From Obstructions
• Generating AdS String Solutions
• Generalized Unitarity and Six-Dimensional Helicity
• Two-Loop Polygon Wilson Loops in N=4 SYM
• On the Strong Coupling Scaling Dimension of High Spin Operators
• One-Loop Superconformal and Yangian Symmetries of Scattering Amplitudes in N=4 Super Yang-Mills
• Amplitudes and Correlators to Ten Loops Using Simple, Graphical Bootstraps
• Color/kinematics duality for general abelian orbifolds of N=4 super Yang-Mills theory
• The Strong Coupling Limit of the Scaling Function from the Quantum String Bethe Ansatz
• A Generalized Scaling Function for AdS/CFT
• Four-loop photon quark form factor and cusp anomalous dimension in the large-$N_c$ limit of QCD
• Higgs-regularized three-loop four-gluon amplitude in N=4 SYM: exponentiation and Regge limits
• Multi-Regge kinematics and the moduli space of Riemann spheres with marked points
• On form factors in N=4 sym
• Complete 1-loop test of AdS/CFT
• Spinor Helicity and Dual Conformal Symmetry in Ten Dimensions
• The Four-Loop Konishi in N=4 SYM
• Generic multiloop methods and application to N=4 super-Yang-Mills
• On T-Duality and Integrability for Strings on AdS Backgrounds
• Scattering in Mass-Deformed N>=4 Chern-Simons Models
• Strong-coupling expansion of cusp anomaly from quantum superstring
• Scattering amplitudes: the most perfect microscopic structures in the universe
• Quantum spectral curve as a tool for a perturbative quantum field theory
• The Dressing Factor and Crossing Equations
• Dual Conformal Properties of Six-Dimensional Maximal Super Yang-Mills Amplitudes
• The two-loop five-point amplitude in $\mathcal{N}=8$ supergravity
• Gauge invariant finite size spectrum of the giant magnon
• Strong coupling limit of Bethe Ansatz equations
• Numerical Evaluation of Tensor Feynman Integrals in Euclidean Kinematics
• Integrability of scattering amplitudes in N=4 SUSY
• The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops
• The four-loop cusp anomalous dimension in N=4 super Yang-Mills and analytic integration techniques for Wilson line integrals
• Spinning superstrings at two loops: strong-coupling corrections to dimensions of large-twist SYM operators
• Twistor-Strings, Grassmannians and Leading Singularities
• D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops
• N >= 4 Supergravity Amplitudes from Gauge Theory at One Loop
• The Four-Loop Dressing Phase of N=4 SYM
• More loops and legs in Higgs-regulated N=4 SYM amplitudes
• Leading Singularities of the Two-Loop Six-Particle MHV Amplitude
• Twist-three at five loops, Bethe Ansatz and wrapping
• Perturbation Theory at Eight Loops: Novel Structures and the Breakdown of Manifest Conformality
• Nine-Propagator Master Integrals for Massless Three-Loop Form Factors
• One-loop one-point functions in gauge-gravity dualities with defects
• Four-Loop Nonplanar Cusp Anomalous Dimension in N=4 Supersymmetric Yang-Mills Theory
• World-sheet scattering in AdS_5 x S^5 at two loops
• Asymptotic one-point functions in AdS/dCFT
• On MHV Form Factors in Superspace for $\mathcal{N}=4$ SYM Theory
• Ten dimensional symmetry of N=4 SYM correlators
• Functional BES equation
• Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division
• On Drinfeld's second realization of the AdS/CFT su(2|2) Yangian
• Simple loop integrals and amplitudes in N=4 SYM
• The Sudakov form factor at four loops in maximal super Yang-Mills theory
• The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM
• Two-Loop Maximal Unitarity with External Masses
• Matter Dependence of the Three-Loop Soft Anomalous Dimension Matrix
• Loops on the Celestial Sphere
• Iterated amplitudes in the high-energy limit
• Quantum integrability and functional equations
• A note on the UV behaviour of maximally supersymmetric Yang-Mills theories
• How tropical are seven- and eight-particle amplitudes?
• Six-Photon Amplitudes
• Three-Loop Leading Singularities and BDS Ansatz for Five Particles
• Regge behavior of gluon scattering amplitudes in N=4 SYM theory
• On the Structure of Supersymmetric Sums in Multi-Loop Unitarity Cuts
• Supersymmetric Wilson loops at two loops
• Spiky strings, light-like Wilson loops and pp-wave anomaly
• Amplitudes and Ultraviolet Behavior of N=8 Supergravity
• Classical r-matrix of the su(2|2) SYM spin-chain
• The scaling function at strong coupling from the quantum string Bethe equations
• A Secret Symmetry of the AdS/CFT S-matrix
• Lifting Heptagon Symbols to Functions
• New Dual Conformally Invariant Off-Shell Integrals
• Review of AdS/CFT Integrability, Chapter III.3: The dressing factor
• Long-range SL(2) Baxter equation in N=4 super-Yang-Mills theory
• Multiple Series Representations of $N$-fold Mellin-Barnes Integrals
• Master integrals for the four-loop Sudakov form factor
• Glauber - Gribov approach for DIS on nuclei in N=4 SYM
• The Six-Point NMHV amplitude in Maximally Supersymmetric Yang-Mills Theory
• Dual conformal symmetry at loop level; massive regularization
• Four-Loop Collinear Anomalous Dimension in N = 4 Yang-Mills Theory
• A First Course on Twistors, Integrability and Gluon Scattering Amplitudes
• A Yangian Double for the AdS/CFT Classical r-matrix
• On the structure of scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity
• Duality between Wilson loops and gluon amplitudes
• The Four-Loop Cusp Anomalous Dimension from the $\mathcal{N}=4$ Sudakov Form Factor
• Twist 3 of the sl(2) sector of N=4 SYM and reciprocity respecting evolution
• Review of AdS/CFT Integrability, Chapter IV.1: Aspects of Non-Planarity
• One-Loop Amplitudes in N=4 Super Yang-Mills and Anomalous Dual Conformal Symmetry
• Nonperturbative Negative Geometries: Amplitudes at Strong Coupling and the Amplituhedron
• Pomeron in the N=4 supersymmetric gauge model at strong couplings
• Fine structure of anomalous dimensions in N=4 super Yang-Mills theory
• On Symmetry Enhancement in the psu(1,1|2) Sector of N=4 SYM
• The virtual scaling function of AdS/CFT
• Singularities of eight- and nine-particle amplitudes from cluster algebras and tropical geometry
• T-Duality, Dual Conformal Symmetry and Integrability for Strings on AdS_5 x S^5
• The Resurgence of the Cusp Anomalous Dimension
• Finite-Size Effects for Multi-Magnon States
• Dual Conformal Structure Beyond the Planar Limit
• Nonperturbative scales in AdS/CFT
• Three loop anomalous dimensions of twist-3 gauge operators in N=4 SYM
• Interacting finite-size magnons
• Antipodal Self-Duality for a Four-Particle Form Factor
• Gluon Reggeization in Yang-Mills Theories
• Anomalous dimensions at twist-3 in the sl(2) sector of N=4 SYM
• Zero modes for the giant magnon
• Analytic solution of the multiloop Baxter equation
• The seven-gluon amplitude in multi-Regge kinematics beyond leading logarithmic accuracy
• Multi-Regge Limit of the Two-Loop Five-Point Amplitudes in $\mathcal{N}=4$ Super Yang-Mills and $\mathcal{N}=8$ Supergravity
• Leading transcedental contribution to the four-loop universal anomalous dimension in N=4 SYM
• Quasilocality of joining/splitting strings from coherent states
• Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes
• Luescher formula for GKP string
• Supersymmetric Wilson loops in N=4 SYM and pure spinors
• All-Mass $n$-gon Integrals in $n$ Dimensions
• Conformal SO(2,4) Transformations of the One-Cusp Wilson Loop Surface
• Maximal Unitarity for the Four-Mass Double Box
• Review of AdS/CFT Integrability, Chapter V.2: Dual Superconformal Symmetry
• Factorized world-sheet scattering in near-flat AdS_5 x S^5
• Testing high-energy factorization beyond the next-to-leading-logarithmic accuracy
• Baxter equation for long-range SL(2|1) magnet
• Non-Chiral S-Matrix of N=4 Super Yang-Mills
• Twist operators in N=4 beta-deformed theory
• Cluster Algebras and the Subalgebra Constructibility of the Seven-Particle Remainder Function
• Superspace calculation of the three-loop dilatation operator of N=4 SYM theory
• Surprises from the resummation of ladders in the ABJ(M) cusp anomalous dimension
• One-loop Wilson loops and the particle-interface potential in AdS/dCFT
• Konishi Form Factor at Three Loop in $\mathcal{N}=4$ SYM
• On DIS Wilson coefficients in N = 4 super Yang-Mills theory
• Dressing the Giant Gluon
• Integrable spin chains and scattering amplitudes
• A Quantum Check of Non-Supersymmetric AdS/dCFT
• What can we learn about QCD and collider physics from N=4 super Yang-Mills?
• Minimal solution of the AdS/CFT crossing equation
• Efficient Evaluation of Massive Mellin--Barnes Integrals
• Prescriptive Unitarity with Elliptic Leading Singularities
• The Two-Loop Remainder Function for Eight and Nine Particles
• Two-Loop Five-Point Two-Mass Planar Integrals and Double Lagrangian Insertions in a Wilson Loop
• The su(2|3) Undynamic Spin Chain
• An Elliptic Yangian-Invariant, `Leading Singularity'
• Cross-Order Integral Relations from Maximal Cuts
• Integrability and non-perturbative effects in the AdS/CFT correspondence
• Review of AdS/CFT Integrability, Chapter V.1: Scattering Amplitudes - a Brief Introduction
• Hidden Simplicity of Gauge Theory Amplitudes
• Inelastic processes in DIS and N=4 SYM
• Aspects of Integrability in AdS/CFT Duality
• IR divergences and Regge limits of subleading-color contributions to the four-gluon amplitude in N=4 SYM Theory
• On the spectral problem of N=4 SYM with orthogonal or symplectic gauge group
• The non-planar contribution to the four-loop anomalous dimension of twist-2 operators: first moments in N=4 SYM and non-singlet QCD
• New four-dimensional integrals by Mellin-Barnes transform
• Non-planar universal anomalous dimension of twist-two operators with general Lorentz spin at four loops in N=4 SYM theory
• On the two-loop divergences of the 2-point hypermultiplet supergraphs for $6D$, $\mathcal{N}=(1,1)$ SYM theory
• Six-loop anomalous dimension of twist-two operators in planar N=4 SYM theory
• Structure of the string R-matrix
• Leading and Subleading UV Divergences in Scattering Amplitudes for D=8 N=1 SYM Theory in All Loops
• Implementation of the Duality between Wilson loops and Scattering Amplitudes in QCD
• Quantum strings in AdS5 x S5 and AdS/CFT duality
• The Effective Action of N=8 Supergravity
• On the Spectrum of the AdS_5xS^5 String at large lambda
• On-shell diagrammatics and the perturbative structure of planar gauge theories
• The Coulomb-branch S-matrix from massless amplitudes
• An Infinite Family of Elliptic Ladder Integrals
• The 2-loop generalized scaling function from the BES/FRS equation
• Superstring in the plane-wave background with RR flux as a conformal field theory
• Review of AdS/CFT Integrability, Chapter III.4: Twist states and the cusp anomalous dimension
• Non-planar anomalous dimension of twist-2 operators: higher moments at four loops
• Wrapping Interactions and the Konishi Operator
• Comment on the Alday-Maldacena solution in calculating scattering amplitude via AdS/CFT
• Challenges of D=6 N=(1,1) SYM Theory
• Fourier transforms of UD integrals
• On string integrability. A journey through the two-dimensional hidden symmetries in the AdS/CFT dualities
• Positivity Sectors and the Amplituhedron
• Form factors with two operator insertions and the principle of maximal transcendentality
• Construction of Infrared Finite Observables in N=4 Super Yang-Mills Theory
• The SAGEX Review on Scattering Amplitudes, Chapter 15: The Multi-Regge Limit
• Sum rules for higher twist sl(2)operators in N=4 SYM
• Conformally Regulated Direct Integration of the Two-Loop Heptagon Remainder
• Infrared Safe Observables in $\mathcal{N}=4$ Super Yang-Mills Theory
• On the origin of the dressing phase in N=4 Super Yang-Mills
• Green-Schwarz superstring on the lattice
• Soft interaction at high energy and N=4 SYM
• Review of AdS/CFT Integrability, Chapter I.2: The spectrum from perturbative gauge theory
• Further results for the two-loop Lcc vertex in the Landau gauge
• From weak coupling to spinning strings
• Testing the nested light-cone Bethe equations of the AdS_5 x S^5 superstring
• Gluon self-interaction in the position space in Landau gauge
• Integrability and the AdS/CFT correspondence
• D-instantons and multiparticle production in N=4 SYM
• 4-particle Amplituhedronics for 3-5 Loops
• Is there a tower of charges to be discovered?
• Generalized Gribov-Lipatov Reciprocity and AdS/CFT
• All-loop Mondrian Reduction of 4-particle Amplituhedron at Positive Infinity
• 6d Dual Conformal Symmetry and Minimal Volumes in AdS
• Scattering amplitudes on the Coulomb branch of N=4 super Yang-Mills
• QCD cusp anomalous dimension: current status
• Dimensional Regularization and Dimensional Reduction in the Light Cone
• 4-particle Amplituhedron at 3-loop and its Mondrian Diagrammatic Implication
• Second order splitting functions and infrared safe cross sections in $\mathcal{N}=4$ SYM theory
• The virtual scaling function of twist operators in the N=6 Chern-Simons theory
• A Two-Loop Four-Point Form Factor at Function Level
• Polylogarithm identities, cluster algebras and the N=4 supersymmetric theory
• The Curious Case of Leading Transcendentality: Three Point Form Factors
• Logarithmic Singularities and Maximally Supersymmetric Amplitudes
• Antipodal self-duality of square fishnet graphs
• On the dressing phase in the SL(2) Bethe Ansatz
• Microscopic formulation of the S-matrix in AdS/CFT
• Twistors, strings and supersymmetric gauge theories
• Aspects of Integrability in N =4 SYM
• Holography on the lattice: the string worldsheet perspective
• Highest states in light-cone $Ad{S}_5\times S^5$ superstring
• Locally Finite Observables in sYM
• DGLAP and BFKL equations in $\mathcal{N}=4$ SYM: from weak to strong coupling
• Multi-fold contour integrals of certain ratios of Euler gamma functions from Feynman diagrams: orthogonality of triangles
• Integrability of the Gauged Linear Sigma Model for AdS_5xS^5
• Algebra of Lax Connection for T-Dual Models
• Loop Amplitudes in the Coulomb Branch of $\mathcal{N}=4$ Super-Yang-Mills Theory
• Integrated Unitarity for Scattering Amplitudes
• On perturbative field theory and twistor string theory
• Supersums for all supersymmetric amplitudes
• Gauge-String Dualities and Some Applications
• Analytic Bethe Ansatz Solutions for Highest States in the su(1|1) and su(2) Sectors
• Perturbative Methods for Superconformal Quantum Field Theories in String - Gauge Theory Dualities
• Infrared Finite Observables in N=8 Supergravity
• Dual Conformal Symmetry and Iterative Integrals in Six Dimensions
• High Energy Behaviour in Maximally Supersymmetric Gauge Theories in Various Dimensions
• N=4 Supersymmetric Yang-Mills theory in soft-collinear effective theory
• Existence of Asymptotic Expansions in Noncommutative Quantum Field Theories
• Discontinuites of BFKL amplitudes and the BDS ansatz
• Divergences in maximal supersymmetric Yang-Mills theories in diverse dimensions
• Topics in Cusped/Lightcone Wilson Loops
• A semiclassical analysis of the fluctuation eigenvalues and the one-loop energy of the folded spinning superstring in AdS_5 x S^5
• On Solving Dual Conformal Integrals in Coulomb-branch Amplitudes and Their Periods
• Integrands of Less-Supersymmetric Yang-Mills at One Loop
• Superstring in the pp-wave background with RR flux as a conformal field theory
• Phase space analysis of Bianchi III Universe with $f(R,T)$ gravity theory
• Duality between Wilson Loops and Scattering Amplitudes
• On interpolating anomalous dimension of twist-two operators with general spins