The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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New Recursion Relations for Tree Amplitudes of Gluons
22 Pith papers cite this work, alongside 1,065 external citations. Polarity classification is still indexing.
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Pith papers citing it
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abstract
We present new recursion relations for tree amplitudes in gauge theory that give very compact formulas. Our relations give any tree amplitude as a sum over terms constructed from products of two amplitudes of fewer particles multiplied by a Feynman propagator. The two amplitudes in each term are physical, in the sense that all particles are on-shell and momentum conservation is preserved. This is striking, since it is just like adding certain factorization limits of the original amplitude to build up the full answer. As examples, we recompute all known tree-level amplitudes of up to seven gluons and show that our recursion relations naturally give their most compact forms. We give a new result for an eight-gluon amplitude, A(1+,2-,3+,4-,5+,6-,7+,8-). We show how to build any amplitude in terms of three-gluon amplitudes only.
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On-shell three-point bootstrap recovers Weyl, chiral, diffeomorphism and Lorentz anomalies up to constant prefactors and reproduces gauge-anomaly cancellation while excluding Pontryagin densities from the Weyl anomaly.
Introduces a bridge transformation on the orthogonal Grassmannian to produce an algebraic recursion for cosmological correlators and identifies the stripped four-gluon correlator as the canonical form of a rectangle in positive geometry.
An on-shell construction using BCFW trees plus vacuum-pair phase-space integrals with inclusion-exclusion signs reproduces the known one- and two-loop all-plus four-gluon amplitudes.
Introduces spectral dispersion bootstrap combining dS spectral decomposition and dispersion relations to compute 3- and 4-point loop correlators with massive scalar and vector exchanges.
Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.
Derives the fundamental BCJ relation at tree level from soft theorems in bi-adjoint scalar theory, generalizes it to 1-loop integrands, and uses it to explain Adler zeros in other scalar theories.
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 determine all tree-level NLSM amplitudes.
Reconstruction of known soft factors via transmutation operators and proof of nonexistence of higher-order universal soft factors for YM and GR amplitudes.
Derives expansion formulas for multi-trace YMS amplitudes bottom-up from soft gluon and scalar behaviors.
A recursive construction expands tree YM amplitudes to YMS and BAS amplitudes from soft theorems while preserving gauge invariance at each step.
Perturbiner multi-particle solutions of classical field equations generate Berends–Giele currents and tree-level amplitudes across scalars, gauge theory, gravity, NLSM, AdS, and one-loop integrands, including several unpublished recursions.
Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.
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 kinematic relation linking YM gauge invariance to NLSM Adler zero.
Recursive construction of off-shell NLSM and SG tree amplitudes from bootstrapped low-point ones via universal soft behaviors, automatically producing enhanced Adler zeros on-shell.
The paper constructs general tree NLSM amplitudes via an expanded formula enforced by Adler zero universality and derives the corresponding double soft factors.
Tree-level amplitudes for Yang-Mills-scalar, pure Yang-Mills, Einstein-Yang-Mills and gravitational theories are reconstructed from soft theorems, universality of soft factors and double copy, with explicit soft factors determined.
Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.
Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.
Extends soft-behavior approach to construct tree YM and YMS amplitudes with F^3 (and F^3+F^4) insertions as universal expansions, plus a conjectured general formula for higher-mass-dimension YM amplitudes from ordinary ones.
A recursive expansion of single-trace YMS amplitudes is built from soft theorems; the result is gauge invariant, permutation symmetric, and equivalent to the Cheung-Mangan covariant color-kinematic duality construction.
citing papers explorer
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String Theory from Maximal Supersymmetry
The open string Veneziano amplitude emerges as the unique tree-level completion of N=4 super Yang-Mills when supersymmetry, factorization, and positivity are imposed.
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Quantum anomalies from three-point on-shell bootstrap
On-shell three-point bootstrap recovers Weyl, chiral, diffeomorphism and Lorentz anomalies up to constant prefactors and reproduces gauge-anomaly cancellation while excluding Pontryagin densities from the Weyl anomaly.
-
A Cosmological BCFW Bridge and Its Canonical Geometry
Introduces a bridge transformation on the orthogonal Grassmannian to produce an algebraic recursion for cosmological correlators and identifies the stripped four-gluon correlator as the canonical form of a rectangle in positive geometry.
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Perturbative construction of amplitudes from on-shell trees with vacuum pairs: the all-plus four-gluon amplitude through order $\boldsymbol{g}^{\boldsymbol{6}}$
An on-shell construction using BCFW trees plus vacuum-pair phase-space integrals with inclusion-exclusion signs reproduces the known one- and two-loop all-plus four-gluon amplitudes.
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On-Shell Bootstrap of Loop Inflation Correlators with Spectral Dispersion
Introduces spectral dispersion bootstrap combining dS spectral decomposition and dispersion relations to compute 3- and 4-point loop correlators with massive scalar and vector exchanges.
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Understanding zeros and splittings of ordered tree amplitudes via Feynman diagrams
Three universal Feynman diagram cuttings explain hidden zeros, 2-splits, and smooth 3-splits in ordered tree amplitudes of Tr(φ³), YM, and NLSM.
-
Tree and $1$-loop fundamental BCJ relations from soft theorems
Derives the fundamental BCJ relation at tree level from soft theorems in bi-adjoint scalar theory, generalizes it to 1-loop integrands, and uses it to explain Adler zeros in other scalar theories.
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A new recursion relation for tree-level NLSM amplitudes based on hidden zeros
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 determine all tree-level NLSM amplitudes.
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On soft factors and transmutation operators
Reconstruction of known soft factors via transmutation operators and proof of nonexistence of higher-order universal soft factors for YM and GR amplitudes.
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Multi-trace YMS amplitudes from soft behavior
Derives expansion formulas for multi-trace YMS amplitudes bottom-up from soft gluon and scalar behaviors.
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Recursive construction for expansions of tree Yang-Mills amplitudes from soft theorem
A recursive construction expands tree YM amplitudes to YMS and BAS amplitudes from soft theorems while preserving gauge invariance at each step.
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Perturbiner methods in scattering amplitude
Perturbiner multi-particle solutions of classical field equations generate Berends–Giele currents and tree-level amplitudes across scalars, gauge theory, gravity, NLSM, AdS, and one-loop integrands, including several unpublished recursions.
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BCFW like recursion for Deformed Associahedron
Adapts BCFW-style recursion to deformed ABHY-associahedron and D-type cluster polytopes for tree-level and one-loop amplitudes in multi-scalar cubic theories.
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Soft theorems of tree-level ${\rm Tr}(\phi^3)$, YM and NLSM amplitudes from $2$-splits
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 kinematic relation linking YM gauge invariance to NLSM Adler zero.
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New recursive construction for tree NLSM and SG amplitudes, and new understanding of enhanced Adler zero
Recursive construction of off-shell NLSM and SG tree amplitudes from bootstrapped low-point ones via universal soft behaviors, automatically producing enhanced Adler zeros on-shell.
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Note on tree NLSM amplitudes and soft theorems
The paper constructs general tree NLSM amplitudes via an expanded formula enforced by Adler zero universality and derives the corresponding double soft factors.
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Tree level amplitudes from soft theorems
Tree-level amplitudes for Yang-Mills-scalar, pure Yang-Mills, Einstein-Yang-Mills and gravitational theories are reconstructed from soft theorems, universality of soft factors and double copy, with explicit soft factors determined.
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Can Locality, Unitarity, and Hidden Zeros Completely Determine Tree-Level Amplitudes?
Locality, unitarity, and hidden zeros determine tree-level YM and NLSM amplitudes by reconstructing their soft theorems.
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Hidden Zeros and $2$-split via BCFW Recursion Relation
Hidden zeros in NLSM amplitudes are proven via modified BCFW recursion, with 2-split holding only under careful current definition.
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Towards tree Yang-Mills and Yang-Mills-scalar amplitudes with higher-derivative interactions
Extends soft-behavior approach to construct tree YM and YMS amplitudes with F^3 (and F^3+F^4) insertions as universal expansions, plus a conjectured general formula for higher-mass-dimension YM amplitudes from ordinary ones.
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Expanding single trace YMS amplitudes with gauge invariant coefficients
A recursive expansion of single-trace YMS amplitudes is built from soft theorems; the result is gauge invariant, permutation symmetric, and equivalent to the Cheung-Mangan covariant color-kinematic duality construction.
- Consistent Scattering Amplitudes, Yang-Mills, the Higgs Mechanism and the EFTs Beyond