Abstract
Supersymmetric integrands for the two-loop five-point amplitudes in ten-dimensional super Yang–Mills and type II supergravity are proposed. The kinematic numerators are manifestly local and satisfy the duality between color and kinematics described by Bern, Carrasco and Johansson. Our results are expected to reproduce the integrated two-loop amplitudes in dimensions D < 7. The UV divergence in the critical dimension D = 7 matches the low-energy limit of the corresponding superstring amplitudes and is written in terms of SYM tree amplitudes.
Highlights
Tree-level and one-loop scattering amplitudes of ten-dimensional super Yang-Mills (SYM) have been recently determined using a method based on two fundamental principles: locality and BRST invariance [1,2,3]
Locality refers to the expansion of amplitudes in terms of cubic graphs with definite propagator structure [4, 5], and BRST invariance is a property of pure spinor superspace that guarantees manifest supersymmetry and gauge invariance [6]
The polarization dependence is furnished by two local kinematic building blocks T12,3|4,5 and T1m,2,3|4,5 written in pure spinor superspace and inspired by string theory whose bosonic components can be downloaded from [11]
Summary
Tree-level and one-loop scattering amplitudes of ten-dimensional super Yang-Mills (SYM) have been recently determined using a method based on two fundamental principles: locality and BRST invariance [1,2,3]. The polarization dependence is furnished by two local kinematic building blocks T12,3|4,5 and T1m,2,3|4,5 written in pure spinor superspace and inspired by string theory whose bosonic components can be downloaded from [11]. Thanks to their compatibility with the Bern-Carrasco-Johansson (BCJ) duality between color and kinematics [4, 5], the corresponding supergravity amplitude is a straightforward corollary [10] and given in (4.16). The same mechanism applies to the one-loop UV divergence, where a prefactor of (8 − D) along with a D-dimensional dilaton reconciles Sduality properties of the superstring amplitude [14, 18] with R-symmetry of supergravity, see appendix C
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