Pith. sign in

REVIEW 15 cited by

Surface Kinematics and "The" Yang-Mills Integrand

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

arxiv 2408.11891 v2 pith:AVRGGDYT submitted 2024-08-21 hep-th hep-ph

Surface Kinematics and "The" Yang-Mills Integrand

classification hep-th hep-ph
keywords integrandsurfaceyang-millsamplitudesconsistentdefinegluonkinematics
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
0 comments
read the original abstract

It has been a long-standing challenge to define a canonical loop integrand for non-supersymmetric gluon scattering amplitudes in the planar limit. Naive integrands are inflicted with $1/0$ ambiguities associated with tadpoles and massless external bubbles, which destroy integrand-level gauge invariance as well as consistent on-shell factorization on single loop-cuts. In this letter, we show that this essentially kinematical obstruction to defining "the" integrand for Yang-Mills theory has a structural solution, handed to us by the formulation of gluon amplitudes in terms of curves on surfaces. This defines "surface kinematics" generalizing momenta, making it possible to define "the" integrand satisfying both a (surface generalized) notion of gauge-invariance and consistent loop-cuts. The integrand also vanishes at infinity in appropriate directions, allowing it to be recursively computed for non-supersymmetric Yang-Mills theory in any number of dimensions. We illustrate these ideas through one loop for all multiplicity, and for the simplest two-loop integrand.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Forward citations

Cited by 15 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. NLSM amplitudes from a quartic two-derivative theory

    hep-th 2026-07 conditional novelty 7.0

    A two-field scalar theory with a single quartic two-derivative vertex reproduces all planar NLSM tree amplitudes and, up to scaleless terms, all loop integrands.

  2. QCD Scattering Amplitudes and Prescriptive Unitarity

    hep-th 2026-02 conditional novelty 7.0

    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.

  3. Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams

    hep-th 2024-11 unverdicted novelty 7.0

    Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.

  4. From Cosmological Cuts to Yang--Mills Wavefunctions in de Sitter Space

    hep-th 2026-06 accept novelty 6.5

    Tree-level Yang-Mills de Sitter wavefunctions through six points are reconstructed from cosmological cuts into cut-detectable gluings plus a current-conservation completion, matching Feynman rules and suggesting an al...

  5. Planar loop integrands from cuts in $D$ dimensions

    hep-th 2026-06 unverdicted novelty 6.0

    A Möbius-inversion formula on the refinement poset reconstructs planar L-loop n-point integrands as sums over non-scaleless scalar graphs dressed by D-dimensional cuts, demonstrated for Yang-Mills theory.

  6. From Cosmological Cuts to Yang--Mills Wavefunctions in de Sitter Space

    hep-th 2026-06 unverdicted novelty 6.0

    Reconstructs four- to six-gluon wavefunctions in de Sitter space from cosmological cuts, separating cut-detectable parts from completions fixed by current conservation and flat-space limit, matching Feynman rules.

  7. Universal Interpretation of Hidden Zero and $2$-Split of Tree-Level Amplitudes Using Feynman Diagrams, Part $\mathbf{I}$: ${\rm Tr}(\phi^3)$, NLSM and YM

    hep-th 2026-04 unverdicted novelty 6.0

    A universal diagrammatic interpretation unifies hidden zeros (from massless on-shell conditions) and 2-splits (from double-line separation) in Tr(φ³), NLSM, and YM tree amplitudes using extended shuffle factorization ...

  8. On differential operators for scalar-scaffolded gluons

    hep-th 2025-12 conditional novelty 6.0

    Differential operators on scalar-scaffolded variables extract individual phi^3 diagrams from gluon amplitudes, and the independent mixed amplitudes are counted by Catalan numbers.

  9. Hidden zeros for higher-derivative YM and GR amplitudes at tree-level

    hep-th 2025-10 unverdicted novelty 6.0

    Hidden zeros extend to higher-derivative tree-level gluon and graviton amplitudes, with systematic cancellation of propagator singularities shown via bi-adjoint scalar expansions.

  10. A new recursion relation for tree-level NLSM amplitudes based on hidden zeros

    hep-th 2025-08 unverdicted novelty 6.0

    A recursion for NLSM tree amplitudes based on hidden zeros reproduces the Adler zero, generates amplitudes from Tr(φ³) via δ-shift, expands them into bi-adjoint scalars, and claims these plus factorization uniquely de...

  11. The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables

    hep-th 2025-05 unverdicted novelty 6.0

    A new formalism with graded inverse variables refines the ℓ-loop planar integrand recursion in bi-adjoint scalar theory, allowing graph factors and symmetry factors to be read directly from monomials.

  12. Systematic approach to $\ell$-loop planar integrands from the classical equation of motion

    hep-th 2025-04 unverdicted novelty 6.0

    A recursion formula for ℓ-loop planar integrands in colored QFTs is derived from the classical equation of motion via comb components and loop kernels.

  13. Off-shell recursion for all-loop planar integrands in Yang-Mills theory

    hep-th 2026-04 unverdicted novelty 5.0

    Yang-Mills planar loop integrands admit an off-shell recursion that organizes the pure-gluon sector into matrix form and incorporates ghost contributions, yielding a concrete two-loop strategy.

  14. $2$-split from Feynman diagrams and Expansions

    hep-th 2025-08 unverdicted novelty 5.0

    Proof via Feynman diagrams that tree-level BAS⊕X amplitudes with X=YM,NLSM,GR obey 2-split under kinematic conditions, extended to pure X amplitudes with byproduct universal expansions of X currents into BAS currents.

  15. Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits

    hep-th 2025-05 unverdicted novelty 5.0

    Extends a 2-split factorization approach to reproduce known leading and sub-leading soft theorems for Tr(φ³) and YM single-soft and NLSM double-soft amplitudes while deriving higher-order universal forms and a kinemat...