algebraic quantum field theory (perturbative, on curved spacetimes, homotopical)
quantum mechanical system, quantum probability
interacting field quantization
general mechanisms
electric-magnetic duality, Montonen-Olive duality, geometric Langlands duality
string-fivebrane duality
string-QFT duality
QFT-QFT duality:
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
Seiberg duality (swapping NS5-branes)
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.
effective QFT incarnations of open/closed string duality,
relating (super-)gravity to (super-)Yang-Mills theory:
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)
As an isomorphism of Lie algebras:
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
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
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: