REVIEW 20 cited by
Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original abstract
We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.
Forward citations
Cited by 20 Pith papers
-
Two-loop four-point amplitudes on the Coulomb branch of ${\mathcal{N}}=4$ super Yang-Mills
The subleading Regge-limit exponent of a Coulomb branch four-point amplitude in N=4 SYM matches the anomalous dimension of a cusped Wilson loop with a scalar insertion, known from integrability.
-
Black Hole Binary Dynamics from the Double Copy and Effective Theory
The authors derive the complete conservative two-body Hamiltonian for spinless black holes at third post-Minkowskian order using scattering amplitudes and effective field theory.
-
Five legs @ three loops: N=4 sYM amplitude near mass-shell
Three-loop five-leg amplitude in planar N=4 sYM near mass shell is computed via 6D unitarity cuts and dimensional reduction, confirming IR exponentiation governed by octagon anomalous dimension with each of three kine...
-
Walking Sudakov: From Cusp to Octagon
In a novel scaling limit on the Coulomb branch of planar N=4 SYM, the Sudakov form factor and four-point amplitude exhibit double-logarithmic behavior governed by a walking anomalous dimension that interpolates betwee...
-
QCD Scattering Amplitudes and Prescriptive Unitarity
The maximally-transcendental part of planar two-loop six-gluon MHV QCD amplitudes is bootstrapped at symbol level and expressed in a 137-letter alphabet.
-
Double spacelike collinear limits from multi-Regge kinematics
The double spacelike collinear limit of planar N=4 SYM is governed by a generalized splitting amplitude that equals the six-point BDS-subtracted amplitude in multi-Regge kinematics.
-
The Two-Loop Lipatov Vertex in QCD
The two-loop Reggeon-gluon-Reggeon (Lipatov) vertex in QCD is determined in dimensional regularization through finite terms and expressed in single-valued polylogarithms.
-
Two-loop MHV Form Factors from the Periodic Wilson Loop
The periodic Wilson loop duality is extended beyond one loop, yielding the two-loop n-particle MHV form factor integrand and new five- and six-particle symbols.
-
Collinear anatomy
Derives a collinear factorization formula for near-mass-shell amplitudes in N=4 SYM, including a new ultrasoft correction to the one-loop splitting amplitude.
-
Eight loop form factors, amplitudes and patterns in planar $\mathcal{N}=4$ super-Yang-Mills theory
Eight-loop computation of the tr φ³ three-point form factor in planar N=4 SYM together with coefficient patterns in its symbol.
-
Soft Algebra for ${\cal N}=4$ SYM
In planar N=4 SYM the IR-finite hard amplitude satisfies an uncorrected tree-level soft theorem and represents the undeformed tree-level S-algebra of soft gluons.
-
On Carrollian Loop Amplitudes for Gauge Theory and Gravity
Loop-level Carrollian amplitudes in N=4 SYM and N=8 supergravity are differential operators on tree-level versions, with logarithmic eikonal behavior and IR-safe factorization via natural splitting.
-
Global Convergence of the Return Dynamics in the Class $\mathcal{O}_C$
Return dynamics on class O_C domains with fixed convex core converge globally like adaptive gradient descent of the thickness function, with fixed points equal to thickness critical points.
-
Relativistic Particle on Light-Front
A front-form construction with a reference null vector makes the massive-to-massless Wigner classification continuous and derives the massless spin-1 polarization shift coefficient from the angle between reference vectors.
-
Regge poles and cuts and the Lipatov vertex
A two-loop multi-Reggeon exchange contribution to 2->3 amplitudes is computed for the first time, enabling extraction of the two-loop Lipatov vertex.
-
Off-shell minimal form factors
Off-shell minimal form factors in planar N=4 SYM exponentiate at two loops with the octagon anomalous dimension; their finite remainder shares the conformal symbol but differs beyond it.
-
Null limit of large-charge correlators in planar $\mathcal{N}=4$ Super-Yang-Mills theory
Conjecture predicts all-loop double-log null-limit behavior of n-point large-charge correlators in planar N=4 SYM via the tilted cusp anomalous dimension, matching small-mass massive amplitudes.
-
Tracing Transcendentality in Protected Correlators of N=4 SYM
Explicit two-loop computations of protected correlators in N=4 SYM yield a universal one-loop term and a planar extrapolation at arbitrary dimension controlled by stress-tensor multiplet count.
-
Multi-Loop Negative Geometries
Explicit three-loop computation of negative geometries for F(g,z) with all-loop resummation of one-cycle diagrams and extraction of the cusp anomalous dimension via z-integration.
-
A simple way to reduce the number of contours in the multi-fold Mellin-Barnes integrals
A five-fold Mellin-Barnes integral for the massless box diagram is reduced to a two-fold triangle integral using analytical regularization and residue calculus, without Barnes lemmas.
Discussion (0). Continue with ORCID to comment.