KLT relations


Quantum Field Theory

algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)



field theory:

Lagrangian field theory


quantum mechanical system, quantum probability

free field quantization

gauge theories

interacting field quantization



States and observables

Operator algebra

Local QFT

Perturbative QFT

Duality in string theory



In perturbative quantum field theory the KLT relations (Kawai-Lewellen-Tye 86) express tree level scattering amplitudes in (super-)gravity equivalently as squares of scattering amplitudes in (super-)Yang-Mills theory.

These relations are manifest in perturbative string theory-UV-completions of Einstein-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 cylinder-shaped worldvolume may be read in two different ways: either as a closed string propagator or as an open string vacuum diagram. This open/closed string duality of string scattering amplitudes yields the KLT relations.

Moreover, a color-kinematics duality suggest that these relations extend from tree level to all loop order.

Its classical field theory counterpart is named classical double copy.


KLT Relations

The original article is

See also

As an isomorphism of Lie algebras:

Gravity amplitudes as double copy Yang-Mills amplitudes

The extension of the KLT relation beyond tree level to “quantum gravity is Yang-Mills squared” (“double copy” approach) originates with

and is further discussed in

Discussion in terms of superstring scattering amplitudes is in

Application to computation of (classical) gravitational wave-signatures from relativistic binary-mergers for used at LIGO: