KLT and New Relations for N=8 SUGRA and N=4 SYM

TL;DR

Addresses how to relate N=8 SUGRA tree amplitudes to N=4 SYM amplitudes within the S-matrix program, avoiding Lagrangians or strings. The authors derive supersymmetric KLT relations by applying SUSY-BCFW recursion to on-shell superamplitudes and organize the result with an S kernel, achieving both (n-2)!- and (n-3)!-symmetric forms. These relations unify earlier non-supersymmetric KLT results and new gauge-theory identities, and they imply additional vanishing identities for scalars and fermions, effectively reducing helicity basis. The work thus provides a field-theoretic, recursion-based bridge between gravity and gauge amplitudes and points to practical simplifications for amplitude calculations.

Abstract

In this short note, we prove the supersymmetric Kawai-Lewellen-Tye (KLT) relations between N=8 supergravity (SUGRA) and N=4 super Yang-Mills (SYM) tree-level amplitudes in the frame of S-matrix program, especially we do not use string theory or the explicit Lagrangian form of corresponding theories. Our supersymmetric KLT relations naturally unify the non-supersymmetric KLT relations and newly discovered gauge theory identities and produce more identities for amplitudes involving scalars and fermions. We point out also that these newly discovered identities can be used to reduce helicity basis from (n-3)! further down.