{"arxiv_id":"hep-th/9811140","incoming":{"papers":153,"sentences":290,"groups":[{"kind":"extends","label":"Builds on it","papers":1,"sentences":1,"quotes":[{"arxiv_id":"2608.26242","title":"The facts on quantum self-dual Einstein gravity and self-dual Yang-Mills theory","url":"/paper/2608.26242","section":"SDG double-off-shell current calculation","sentence":"This computation was sketched in words in [ref] and we are told the authors performed the computation for $n=4,5$, but here we carry it out to all $n$.","intent_p":0.99,"contests_p":null}]},{"kind":"method_or_tool","label":"Uses its method or tool","papers":13,"sentences":13,"quotes":[{"arxiv_id":"2503.15662","title":"Color-kinematics and double-copy relations for selfdual solutions","url":"/paper/2503.15662","section":"Double-copy form","sentence":"To write the gravity kernel in a double-copied form, we first perform a basis expansion of the Lie polynomial $b(P)$ in ([ref]): [equation] As shown in [ref] , this relation can be inverted to obtain the kinematic numerator $n^p ( ℓ[1Q] )$ by means the KLT matrix $S(P|Q)_1$ [ref] : [equation] Substituting in ([ref]) we obtain a double-copy form for the gravity kernel, expressed in terms two copies of the color-stripped Yang-Mills kernel and the KLT matrix: [equation] To make the expression fully explicit, we recall from ([ref], [ref]) that [equation] and that the KLT matrix is given by [ref] [equation] where $θ(i_t, i_q)$ is 0 if $i_t$ sequentially comes before $i_q$ in ${j_1, …, j_k}$, and 1 otherwise.","intent_p":0.81,"contests_p":null},{"arxiv_id":"0812.4533","title":"A Note on Single Soft Scalar Emission of $\\mathcal{N}=8$ SUGRA and $E_{7(7)}$ Symmetry","url":"/paper/0812.4533","section":"Introduction","sentence":"We shall use a simple formula for general one-loop amplitude in terms of tree amplitudes [ref] follows from “no triangle hypothesis” [ref] .","intent_p":0.81,"contests_p":null},{"arxiv_id":"2112.15029","title":"The KLT Relation from the Tree formula and Permutohedron","url":"/paper/2112.15029","section":"Introduction","sentence":"This paper explores the KLT relation in these aspects by referring to the NSVW/BDPR tree formula [ref] to discuss the tree structure of the KLT relation.","intent_p":0.9,"contests_p":null},{"arxiv_id":"1011.2487","title":"On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes","url":"/paper/1011.2487","section":"Explicit proof","sentence":"To do so, we use the helicity spinor formalism and the Parke-Taylor formula [ref] , which states that A_n(1^+2^+...i^-...j^-...n^+)=⟨ij⟩^4/⟨12⟩⟨23⟩...⟨n1⟩ or for our case, for instance choosing $1^-2^-$, A_5(1^-2^-3^+4^+5^+)=⟨12⟩^4/⟨12⟩⟨23⟩⟨34⟩⟨45⟩⟨51⟩ A similar formula exists for the supergravity amplitude [ref] M_5(1^-2^-3^+4^+5^+)=⟨12⟩^8ϵ(1234)/N(5) where ϵ(ijkl) = 4iϵ_μνρσk_i^μk_j^νk_k^ρk_l^σN(5) = ∏_i=1^4∏_j=i+1^5⟨ij⟩","intent_p":0.95,"contests_p":null},{"arxiv_id":"2111.15649","title":"Kinematic Hopf Algebra for BCJ Numerators in Heavy-Mass Effective Field Theory and Yang-Mills Theory","url":"/paper/2111.15649","section":"Appendix: Factorisation of BCJ numerators from KLT relations","sentence":"Using Eq. [ref], the known factorisation of HEFT amplitudes, and the recursive relation for the KLT matrix [ref] [equation] one finally arrives at Eq. [ref].","intent_p":0.81,"contests_p":null}]},{"kind":"data_used","label":"Uses its data or values","papers":2,"sentences":2,"quotes":[{"arxiv_id":"2009.07881","title":"Descendants in celestial CFT and emergent multi-collinear factorization","url":"/paper/2009.07881","section":"Multi-collinear factorization","sentence":"The double-collinear limits that we need are given by [ref] ^(2)_+ = -κ/2 z̅_12/z_12 (ω_1+ω_2)^2/ω_1 ω_2 , ^(2)_-(1^-) = -κ/2 z̅_12/z_12 ω_1^3/ω_2 (ω_1+ω_2)^2 .","intent_p":0.9,"contests_p":null},{"arxiv_id":"2105.05218","title":"The Amplitude for Classical Gravitational Scattering at Third Post-Minkowskian Order","url":"/paper/2105.05218","section":"The five-point tree amplitude and the three-graviton cut","sentence":"The singlet amplitude is the one given in [ref] .","intent_p":0.81,"contests_p":null}]},{"kind":"comparison","label":"Compares with it","papers":14,"sentences":22,"quotes":[{"arxiv_id":"2103.16984","title":"Twistor sigma models for quaternionic geometry and graviton scattering","url":"/paper/2103.16984","section":"MHV scattering","sentence":"We then obtain the amplitude as a tree expansion via the standard field theory tree expansion of the sigma model, making contact with the formulae of [ref] .","intent_p":0.85,"contests_p":null},{"arxiv_id":"1410.5647","title":"Pure connection formalism for gravity: Recursion relations","url":"/paper/1410.5647","section":"Introduction","sentence":"Our computation of the off-shell gauge-theoretic current leads to an essentially the same recursion relation that appears in [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"0906.2526","title":"Holonomies of gauge fields in twistor space 2: Hecke algebra, diffeomorphism, and graviton amplitudes","url":"/paper/0906.2526","section":"Gravitational holonomy operators","sentence":"Indeed, the structure of the Chan-Paton factor in ([ref]) is the same as that of graviton amplitudes which has been obtained by Bern et al. in [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1509.04483","title":"An Algebraic Approach to the Scattering Equations","url":"/paper/1509.04483","section":"Gravity and $n$-point KLT Relations","sentence":"which agrees perfectly with the result given by KLT relation [ref] .","intent_p":1.0,"contests_p":null},{"arxiv_id":"1008.1626","title":"Note on New KLT relations","url":"/paper/1008.1626","section":"From $S_n-2$ KLT to $S_n-3$ KLT","sentence":"Comparing to the formula given in [ref] , formula ([ref]) is much easy to prove using BCFW recursion relations in field theory while its stringy derivation is still missing.","intent_p":0.99,"contests_p":null}]},{"kind":"supports_this_paper","label":"Cites it as support","papers":1,"sentences":1,"quotes":[{"arxiv_id":"0808.1446","title":"What is the Simplest Quantum Field Theory?","url":"/paper/0808.1446","section":"Absence of Rational Terms","sentence":"The structure of the soft (also given in [ref] ) and collinear limits give additional evidence for the extra simplicity of gravity compared to gauge theory: remarkably, the soft factors and collinear splitting functions are not renormalized beyond tree level, as a direct consequence of the dimensionful coupling constant in gravity!","intent_p":0.96,"contests_p":null}]},{"kind":"background","label":"Cites it as background","papers":56,"sentences":63,"quotes":[{"arxiv_id":"2212.11480","title":"Soft and Collinear Limits in $\\mathcal{N}=8$ Supergravity using Double Copy Formalism","url":"/paper/2212.11480","section":"Double copy and collinear limit","sentence":"Once the large string tension limit (also called the field theory limit) is taken, the KLT relation turns into a relation between gravity and gauge theory tree level amplitudes [ref] .","intent_p":0.86,"contests_p":null},{"arxiv_id":"1111.5691","title":"Note on Cyclic Sum and Combination Sum of Color-ordered Gluon Amplitudes","url":"/paper/1111.5691","section":"Introduction","sentence":"On-shell recursion relation for tree-level gluon amplitudes [ref] has been shown to be important not only for real calculations, but also for theoretical understanding of many important properties such as the BCJ relaton [ref] [The BCJ relation has first been proved in string theory [ref] , and then in field theory [ref] .] and Kawai-Lewellen-Tye relation [ref] [See also recent review [ref] .].","intent_p":0.98,"contests_p":null},{"arxiv_id":"1812.03369","title":"String amplitudes from field-theory amplitudes and vice versa","url":"/paper/1812.03369","section":"Introduction","sentence":"The field-theory limit of the celebrated Kawai-Lewellen-Tye (KLT) relations [ref] between tree amplitudes in open and closed string theory gives double copy relations linking gauge-theory amplitudes to gravitational ones [ref] .","intent_p":0.95,"contests_p":null},{"arxiv_id":"1610.04230","title":"Inverse of the String Theory KLT Kernel","url":"/paper/1610.04230","section":"KLT Relations","sentence":"The explicit formula for all multiplicities in the $α' →0$ limit was given in [ref] and later proven in a more general setting in [ref] .","intent_p":0.93,"contests_p":null},{"arxiv_id":"2103.16984","title":"Twistor sigma models for quaternionic geometry and graviton scattering","url":"/paper/2103.16984","section":"MHV scattering","sentence":"Explicit, all-multiplicity formulae for tree-level gravitational MHV amplitudes in flat space have been known for decades [ref] , with the optimal formula (in terms of compactness and explicit permutation symmetry) due to Hodges [ref] .","intent_p":0.89,"contests_p":null}]}],"unlabelled_sentences":188},"outgoing":{"papers":0,"sentences":0,"groups":[],"unlabelled_sentences":0},"claims":[],"thresholds":{"intent_p":0.8,"supports_p":0.95,"contests_p":0.7},"method":"Citing sentences come from each paper's LaTeX source; every \\cite marks the sentence and the works it cites. Pith's classifier typed each sentence. A label is shown at intent probability 0.8 or more (0.95 for support), a contest at 0.7 or more. Measured accuracy against two blind model families is at https://pith.science/accuracy. The quoted sentences are the citing authors' own.","held_up":{"arxiv_id":"hep-th/9811140","kind":"model","paper_version":2,"prompt_version":"held-up-v3.5","generated_at":"2026-10-27T15:03:08+00:00","loaded_at":"2026-10-28T01:02:18.112312+00:00","evidence":"substantial","account":[],"groups":[{"kind":"extends","label":"Builds on it","papers":1,"entries":[{"p":0.99,"quote":null,"citing":[{"self":false,"year":2026,"title":"The facts on quantum self-dual Einstein gravity and self-dual Yang-Mills theory","arxiv_id":"2608.26242"}],"verified":true,"paraphrase":"Carried out to all n a computation that this paper sketched in words and was said to have performed for n=4,5."}],"papers_all":1,"self_papers":0,"self_entries":[]},{"kind":"comparison","label":"Compares with it","papers":1,"entries":[{"p":1.0,"quote":null,"citing":[{"self":false,"year":2014,"title":"Pure connection formalism for gravity: Recursion relations","arxiv_id":"1410.5647"}],"verified":true,"paraphrase":"Said that its computation of the off-shell gauge-theoretic current leads to essentially the same recursion relation that appears in this paper."}],"papers_all":15,"self_papers":0,"self_entries":[]}],"counts":{"by_kind":{"extends":1,"data_used":2,"comparison":15,"method_or_tool":14,"supports_this_paper":2},"dropped":{"relied_on":0,"unknown_ids":0,"account_lines":0,"contest_vetoed":0,"below_threshold":0,"contest_drawback":0,"contest_without_basis":0,"contest_not_one_sentence":0,"contest_on_group_citation":0},"papers_read":15,"self_papers":3,"citing_papers":159,"sentences_read":20,"citing_sentences":295,"unambiguous_read":20,"typed_independent":33,"independent_papers":156,"by_kind_independent":{"extends":1,"data_used":2,"comparison":15,"method_or_tool":14,"supports_this_paper":2}},"input_sha256":"a980384316bb51d1d12faaa7187c44d8c2d9b648b42522bd29a595925468b28f","method":"For a paper with five or more citing arXiv papers, Pith selected up to 40 citing sentences its citation classifier typed, read those whose citation markers point at this paper alone, and wrote one paraphrase for each later paper in each group, each resting on one sentence. A later paper is listed under a label only when the classifier gives one of its sentences that label at intent probability 0.8 or more (0.95 for support), Pith's reading of the sentence finds that the citing paper itself did it, and a second check of the paraphrase against the sentence passes. The section lists uses only: building on the paper, using its method, tool, data or values, comparing with it and citing it as support. It does not list criticism or disagreement, so their absence says nothing about how the paper has been received. Code counted the papers, wrote the summary from the listed entries, set the evidence level and linked each entry to its citing paper. Quotes are copied from the citing sentence and shown only when the citing paper's licence is CC BY, CC BY-SA or CC0; otherwise the paraphrase is shown. Papers that share an author with this one are listed apart. A paper with fewer citing papers gets a line counted by code, which names uses only: a later paper whose only label is a contest is counted as not described.","line":null,"summary":"2 later papers by other authors are listed below: 1 built on it and 1 compared its own results with it."},"_links":{"html":"https://pith.science/paper/hep-th/9811140"}}