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.
Berends-Giele recursions and the BCJ duality in superspace and components
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abstract
The recursive method of Berends and Giele to compute tree-level gluon amplitudes is revisited using the framework of ten-dimensional super Yang-Mills. First we prove that the pure spinor formula to compute SYM tree amplitudes derived in 2010 reduces to the standard Berends-Giele formula from the 80s when restricted to gluon amplitudes and additionally determine the fermionic completion. Second, using BRST cohomology manipulations in superspace, alternative representations of the component amplitudes are explored and the Bern-Carrasco-Johansson relations among partial tree amplitudes are derived in a novel way. Finally, it is shown how the supersymmetric components of manifestly local BCJ-satisfying tree-level numerators can be computed in a recursive fashion.
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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.
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.
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The bi-adjoint scalar $\ell$-loop planar integrand recursion and graded inverse variables
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.
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Systematic approach to $\ell$-loop planar integrands from the classical equation of motion
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.
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Off-shell recursion for all-loop planar integrands in Yang-Mills theory
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.