Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace

TL;DR

This paper proposes supersymmetric integrands for two-loop five-point amplitudes in super Yang-Mills and supergravity, demonstrating local kinematic numerators satisfying color-kinematics duality, with implications for UV divergences and string theory limits.

Contribution

It introduces explicit supersymmetric integrands in pure spinor superspace that satisfy color-kinematics duality for two-loop five-point amplitudes.

Findings

Integrands are local and satisfy color-kinematics duality.

Results reproduce known two-loop amplitudes in dimensions less than 7.

UV divergence in D=7 matches superstring amplitude limits.

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.