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Journal Article

Towards one-loop SYM amplitudes from the pure spinor BRST cohomology


Mafra,  Carlos R.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;


Schlotterer,  Oliver
Quantum Gravity and Unified Theories, AEI Golm, MPI for Gravitational Physics, Max Planck Society;

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Mafra, C. R., & Schlotterer, O. (2015). Towards one-loop SYM amplitudes from the pure spinor BRST cohomology. Fortschritte der Physik, 63(2), 105-131. doi:10.1002/prop.201400076.

Cite as: http://hdl.handle.net/11858/00-001M-0000-0024-2799-A
In this paper, we outline a method to compute supersymmetric one-loop integrands in ten-dimensional SYM theory. It relies on the constructive interplay between their cubic-graph organization and BRST invariance of the underlying pure spinor superstring description. The five- and six-point amplitudes are presented in a manifestly local form where the kinematic dependence is furnished by BRST-covariant expressions in pure spinor superspace. At five points, the local kinematic numerators are shown to satisfy the BCJ duality between color and kinematics leading to supergravity amplitudes as a byproduct. At six points, the sources of the hexagon anomaly are identified in superspace as systematic obstructions to BRST invariance. Our results are expected to reproduce any integrated SYM amplitude in dimensions $D< 8$.