BCJ and KK Relations from BRST Symmetry and Supergravity Amplitudes

TL;DR

This paper derives BCJ and KK relations in supergravity amplitudes using BRST symmetry within Pure Spinor string theory, providing explicit constructions and extending previous methods to 6-point amplitudes.

Contribution

It introduces a novel approach to derive BCJ and KK relations from BRST invariance and computes 6-point supergravity amplitudes from SYM building blocks.

Findings

Explicit construction of kinematical factors satisfying KK relations

Derivation of BCJ and KK identities from BRST invariance

Calculation of 6-point supergravity amplitude from SYM components

Abstract

We use Pure Spinor string theory to construct suitable kinematical factors which explicitly satisfy the Kleiss-Kuijf (KK) relations. Using the formula conceived by Bern et al. and employed by us for 4- and 5-point amplitudes in a previous work, we are able to compute the 6-point supergravity amplitude from the corresponding SYM building blocks given by Mafra et al.. We derive the KK and Bern-Carrasco-Johansson (BCJ) identities from the BRST invariance and we discuss the relations between Bern et al. building blocks and those of Mafra et al..