nLab KLT relations

Idea

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.

Related entries

• magic pyramid

• classical double copy

• string theory results applied elsewhere

• duality in physics

• effective QFT incarnations of open/closed string duality,

  relating (super-)gravity to (super-)Yang-Mills theory:

  • KLT relations

  • BCJ relations

  • classical double copy

References

KLT Relations

The original article is

• Hikaru 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)90362-7)

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, Fortschr. Phys. 59 (2011) 7-8 [arXiv:1103.1848, doi:10.1002/prop.201100037]

  (in D=4 N=8 supergravity)

• 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)

As an isomorphism of Lie algebras:

• Hadleigh Frost, The Algebraic Structure of the KLT Relations for Gauge and Gravity Tree Amplitudes, SIGMA 17 101 (2021) (arXiv:2111.07257)

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 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)

• Alexandros Anastasiou, Leron Borsten, Mike Duff, Alessio Marrani, Silvia Nagy, M. Zoccali, Are all supergravity theories Yang-Mills squared? (arXiv:1707.03234)

• Alexandros Anastasiou, Leron Borsten, Mike J. Duff, M. J. Hughes, A. Marrani, Silvia 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

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude I: Pure spinors and superfield kinematics (arXiv:1812.10969)

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude II: Worldsheet functions and their duality to kinematics (arXiv:1812.10970)

• Carlos Mafra, Oliver Schlotterer, Towards the $n$-point one-loop superstring amplitude III: One-loop correlators and their double-copy structure (arXiv:1812.10971)

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)

Review:

• Zvi Bern, John Joseph Carrasco, Marco Chiodaroli, Henrik Johansson, Radu Roiban, Supergravity amplitudes, the double copy and ultraviolet behavior, in Handbook of Quantum Gravity, Springer (2023) [arXiv:2304.07392]