KLT relations


Algebraic Quantum Field Theory

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



field theory: classical, pre-quantum, quantum, perturbative quantum

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quantum mechanical system, quantum probability

free field quantization

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Perturbative QFT

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 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 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 spring


KLT Relations

The original article is

  • H. Kawai, D.C. Lewellen, S.H.H. Tye, A Relation Between Tree Amplitudes of Closed and Open Strings, Nucl.Phys. B269 (1986) 1-23 (doi:10.1016/0550-3213(86)90362-790362-7))

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)

Gravity amplitudes as Yang-Mills amplitudes “squared”

The extension of the KLT relation beyond tree level to “quantum gravity is Yang-Mills squared” 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

  • 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)

Last revised on February 7, 2018 at 14:29:00. See the history of this page for a list of all contributions to it.