KLT and new relations for $ \mathcal{N} = 8 $ SUGRA and $ \mathcal{N} = 4 $ SYM

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.

The momentum kernel of gauge and gravity theories

“…Then one obtains new non-linear relations among Yang-Mills amplitudes [22] that can be understood in the context of Rcharges [23][24][25][26]. This paper will be devoted to a detailed study of the string theory momentum kernel S α ′ .…”

The construction of dual-trace factor in Yang-Mills theory

“…The newly discovered BCJ relations have been understood both from string [4,5,6] and field theory [7,8,9,10] perspectives. BCJ relations also serve as the key to the understanding of KLT relations [11], which express gravity tree amplitude in terms of products of two color-ordered Yang-Mills tree amplitudes (See [12,13,14,15]). Although a proof at loop-levels is currently absent, explicit calculations show that the duality (1.2) is also satisfied at the first few loops [16,17,18,19,20,21,22,23,24,25].…”

Soft theorems in maximally supersymmetric theories

“…2.3, all derivatives in operators only act on amplitudes. These relations may be derived using the scheme proposed in [19] by super-KLT relation [72,[76][77][78]91,92].…”