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

  • Zvi Bern, Perturbative Quantum Gravity and its Relation to Gauge Theory, LivingRev.Rel.5:5,2002 (arXiv:gr-qc/0206071)

  • 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, The S-matrix reloaded: Twistors, Unitarity, Gauge theories and Gravity, 2005 (pdf)

  • 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)

  • Dhritiman Nandan, Jan Plefka, Oliver Schlotterer, Congkao Wen, Einstein-Yang-Mills from pure Yang-Mills amplitudes (arXiv:1607.05701)

  • Luiz Antonio Barreiro, Ricardo Medina, The origin of the KLT relations and nonlinear relations for Yang-Mills amplitudes (arxiv:1910.13519)

  • Pierre Vanhove, Federico Zerbini, Building blocks of closed and open string amplitudes (arXiv:2007.08981)

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

  • Zvi Bern, John Joseph M. Carrasco, Henrik Johansson, Perturbative Quantum Gravity as a Double Copy of Gauge Theory, Phys. Rev .Lett. 105:061602,2010 (arXiv:1004.0476)

and is further discussed in

  • David C. Dunbar, Paul S. Norridge, Calculation of Graviton Scattering Amplitudes using String-Based Methods, Nucl.Phys. B433 (1995) 181-208 (arXiv:hep-th/9408014)

  • Zvi Bern, D.C. Dunbar, T. Shimada, String-Based Methods in Perturbative Gravity, Phys.Lett.B312:277-284, 1993 (arXiv:hep-th/9307001)

  • A. Anastasiou, L. Borsten, Mike Duff, A. Marrani, S. Nagy, M. Zoccali, Are all supergravity theories Yang-Mills squared? (arXiv:1707.03234)

  • A. Anastasiou, L. Borsten, M. J. Duff, M. J. Hughes, A. Marrani, S. Nagy, M. Zoccali, Twin Supergravities from Yang-Mills Squared, Phys. Rev. D 96, 026013 (2017) (arXiv:1610.07192)

  • A. Anastasiou, L. Borsten, M. J. Duff, S. Nagy, M. Zoccali, BRST squared (arXiv:1807.02486)

  • L. Borsten, Gravity as the square of gauge theory: a review, (doi:10.1007/s40766-020-00003-6)

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:

  • Zvi Bern, Clifford Cheung, Radu Roiban, Chia-Hsien Shen, Mikhail P. Solon, Mao Zeng, Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order, Phys. Rev. Lett. 122, 201603 (2019) (arXiv:1901.04424)

Last revised on July 20, 2020 at 04:32:07. See the history of this page for a list of all contributions to it.