Types of quantum field thories
abstract duality: opposite category,
These relations are manifest in string theory-UV-completions of gravity+Yang-Mills theory, where they were originally found and from which the QFT relations have been deduced: in string theory the graviton is an excitation of the closed string and the gluon of the open string. But disk-shaped string diagram can be read in two-ways: either as a closed-string vacuum diagram or as an open-string tree-level scattering diagram. This open/closed string duality of string scattering amplitudes yields the KLT relations.
N. E. J. Bjerrum-Bohr, K. Risager, String theory and the KLT-relations between gravity and gauge theory including external matter (arXiv:hep-th/0407085)
Zvi Bern, John Joseph Carrasco, Lance Dixon, Henrik Johansson, Radu Roiban, Amplitudes and Ultraviolet Behavior of N=8 Supergravity (arXiv:1103.1848)
Bo Feng, Song He, Rijun Huang, Yin Jia, Note on New KLT relations (arXiv:1008.1626)