Maximal Supergravity at Five Loops !   
Single (top) vs double copy (bottom) theory

This past year a team at IPhT around John Joseph Carrasco — in collaboration with physicists at UCLA and Penn State University in the United States, and Uppsala University in Sweden — completed a calculation long thought to be impossible: the direct understanding of the dimensions of space-time in which the most symmetric particle-based field theory of gravity (maximal supergravity) would cease to be predictive when quantum effects are relevant. One can isolate order by order the quantum effects in graviton scattering. For two gravitons scattering off of each other, this calculation required consideration of the fifth-order quantum correction. This puts strong constraints on the behavior of fundamental symmetries in controlling the high-energy behavior of this theory.
To give an idea of the size of the problem, consider a word count of everything ever written by human beings (from cuneiform tablets and stone carvings to books, magazines, emails, etc). This was estimated at one time to be some 40 quadrillion words. The traditional approach to their calculation would involve writing that many mathematical expressions, 40 quadrillion more times! That’s why it was thought to be impossible — even with the world's most powerful computers.

To carry out this calculation, they instead relied critically on newfound insights as to the local relationship of gravity to the theory that describes how quarks interact via gluons. This is called Double Copy structure. If you successfully carry out a calculation involving gluons, it turns out you can recycle it to make a prediction involving gravitons. Using these ideas effectively turned the impossibly complicated gravity calculation into a much tamer one: a few tens of thousands of expressions. This is less than the number of unique words in the French language! This approach has yielded insights that may prove crucial to the ultimate all order understanding of our ability to make quantum gravity predictions in particle field theory. The very precise form of the double copy structure fits perfectly with the algebraic structures derived from elementary properties of quantum field theory amplitudes.

This work of course does not happen in a vacuum. The field of studying scattering between fundamental particles -- the study of scattering amplitudes -- has seen tremendous progress over the past decades, and the work here builds upon developments pioneered by other members of IPhT, including that of David Kosower, Gregory Korchemsky, and Pierre Vanhove.


[1] Ultraviolet Properties of N=8 Supergravity at Five Loops
By Zvi Bern, John Joseph Carrasco, Wei-Ming Chen, Alex Edison, Henrik Johansson, Julio Parra-Martinez, Radu Roiban, Mao Zeng.
arXiv:1804.09311 [hep-th].
Phys.Rev. D98 (2018) no.8, 086021.

[2] Five-loop four-point integrand of N=8 supergravity as a generalized double copy
By Zvi Bern, John Joseph M. Carrasco, Wei-Ming Chen, Henrik Johansson, Radu Roiban, Mao Zeng.
arXiv:1708.06807 [hep-th].
Phys.Rev. D96 (2017) no.12, 126012.

[3] Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes
By Zvi Bern, John Joseph Carrasco, Wei-Ming Chen, Henrik Johansson, Radu Roiban.
arXiv:1701.02519 [hep-th].
Phys.Rev.Lett. 118 (2017) no.18, 181602.

Earlier related works:

[4] Dual superconformal symmetry of scattering amplitudes in N=4 super-Yang-Mills theory
By J.M. Drummond, J. Henn, G.P. Korchemsky, E. Sokatchev.
arXiv:0807.1095 [hep-th].
Nucl.Phys. B828 (2010) 317-374.

[5] Fusing gauge theory tree amplitudes into loop amplitudes
By Zvi Bern, Lance J. Dixon, David C. Dunbar, David A. Kosower.
Nucl.Phys. B435 (1995) 59-101.

[6] Monodromy and Jacobi-Like Relations for Color-Ordered Amplitudes,
 N. E. J. Bjerrum-Bohr, P. H. Damgaard, T. Sondergaard and P. Vanhove,  
  JHEP 1006 (2010) 003,    [arXiv:1003.2403 [hep-th]].

[7] The Critical Ultraviolet Behaviour of N=8 Supergravity Amplitudes, P. Vanhove,
  arXiv:1004.1392 [hep-th].

C. Pepin, 2018-12-18


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