Abstract
We obtain local numerators satisfying the BCJ color-kinematics duality at one loop for super-Yang-Mills theory in ten dimensions. This is done explicitly for six points via the field-theory limit of the genus-one open superstring correlators for different color orderings, in an analogous manner to an earlier derivation of local BCJ-satisfying numerators at tree level from disk correlators. These results solve an outstanding puzzle from a previous analysis where the six-point numerators did not satisfy the color-kinematics duality.
Highlights
This paper aims to answer a question left over from the pure spinor construction of oneloop integrands of super-Yang-Mills (SYM) using locality and BRST invariance [11]
In this paper we will use the same formalism of multiparticle superfields in pure spinor superspace to present local representations of the five, six- and seven-point amplitudes that do obey the color-kinematics duality
In this work we obtained a set of field-theory limit rules for the Kronecker-Eisenstein coefficient functions present in the genus-one superstring correlators derived in [19,20,21]. Using these rules we found local numerators for ten-dimensional SYM integrands at one loop for five, six and seven points that satisfy the BCJ color-kinematics duality
Summary
This paper aims to answer a question left over from the pure spinor construction of oneloop integrands of super-Yang-Mills (SYM) using locality and BRST invariance [11]. Can one find a set of local and supersymmetric numerators for ten-dimensional SYM one-loop integrands at six points satisfying the Bern-Carrasco-Johansson (BCJ) [6]1 color-kinematics duality? The one-loop integrands of SYM in ten dimensions for five and six points were constructed in [11], where it was shown that the numerators for the five-point amplitude satisfied the color-kinematics duality while those at six points did not. By assembling the numerators of the cubic graphs for all p-gons of a n-point amplitude such that their sum is in the pure spinor BRST cohomology (up to anomalous terms of the form discussed in [26, 27]), the amplitudes of the color-ordered five and six-point amplitudes for the canonical color ordering were constructed. The six-point integrand was later successfully used in [29], passing some consistency checks
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