2008

What is the Simplest Quantum Field Theory?

Arkani-Hamed, Nima, Cachazo, Freddy, Kaplan, Jared

Understand

Conventional wisdom says that the simpler the Lagrangian of a theory the simpler its perturbation theory, but an increased understanding of the structure of the S-matrix in gauge theories and gravity has been pointing to the opposite conclusion.

In this paper we suggest that N=8 SUGRA has the simplest interacting S-matrix in 4D.
Using Grassmann coherent states for external particles shows that amplitudes with maximal SUSY are smooth objects, with the action of SUSY manifest.
We show that all tree amplitudes in N=4 SYM and N=8 SUGRA vanish at (supersymmetric) infinite complex momentum, and can thus be determined by recursion relations.

Built on

R.E. Cutkosky, J.Math. Phys. 1
1960
Earlier work this paper cites.
S. Weinberg, Phys. Rev. 135
1964
Earlier work this paper cites.
S. L. Adler, Phys. Rev. 137
1965
Earlier work this paper cites.
D. I. Olive, “Exploration of S-Matrix Theory,” Phys. Rev. 135, B745 (1964). G. F. Chew, “The Analytic S-Matrix: A Basis for Nuclear Democracy,” W. A. Benjamin, Inc., 1966. R. J. Eden, P. V. Landshoff, D. I. Olive, J. C. Polkinghorne, “The Analytic S-Matrix”, Cambridge University Press, 1966
1966
Earlier work this paper cites.
S. Weinberg, Phys. Rev. Lett. 17
1966
Earlier work this paper cites.
L. Susskind and G. Frye, Phys. Rev. D 1
1970
Earlier work this paper cites.
R. Penrose and M. A. H. MacCallum, Phys. Rept. 6
1972
Earlier work this paper cites.
E. Cremmer and B. Julia, Phys. Lett. B 80
1977
Earlier work this paper cites.
L. Brink, J. H. Schwarz and J. Scherk, Nucl. Phys. B 121
1977
Earlier work this paper cites.
M. B. Green, J. H. Schwarz and L. Brink, Nucl. Phys. B 198
1982
Earlier work this paper cites.
T. Banks and A. Zaks, Nucl. Phys. B 196
1982
Earlier work this paper cites.
S. Mandelstam, Nucl. Phys. B 213
1983
Earlier work this paper cites.
L. Lewin, J. of Number Theory. 19
1984
Earlier work this paper cites.
The use of this fact for the computation of scattering amplitudes goes back to: F. A. Berends, R. Kleiss, P. De Causmaecker, R. Gastmans and T. T. Wu, Phys. Lett. B 103
1985
Earlier work this paper cites.
S. J. Parke and T. R. Taylor, Phys. Rev. Lett. 56
1986
Earlier work this paper cites.
H. Kawai, D. C. Lewellen and S. H. H. Tye, Nucl. Phys. B 269
1986
Earlier work this paper cites.
M. H. Goroff and A. Sagnotti, Nucl. Phys. B 266
1986
Earlier work this paper cites.
F. A. Berends and W. T. Giele, Nucl. Phys. B 306
1988
Earlier work this paper cites.
V. P. Nair, Phys. Lett. B 214
1988
Earlier work this paper cites.
F. Cachazo, arXiv:0803.1988 [hep-th]
Original
1988
Earlier work this paper cites.
Z. Bern and D. A. Kosower, Phys. Rev. Lett. 66
1991
Earlier work this paper cites.
L. Susskind, L. Thorlacius and J. Uglum, Phys. Rev. D 48
1993
Earlier work this paper cites.

Similar

G. Passarino and M. J. G. Veltman, Nucl. Phys. B 160
1994
Cited alongside, same era.
See e.g. S. Weinberg, “The Quantum theory of fields. Vol. 1: Foundations,” Cambridge, UK: Univ. Pr. (1995) 609 p
1995
Cited alongside, same era.
Z. Bern and G. Chalmers, Nucl. Phys. B 447
1995
Cited alongside, same era.
Z. Bern, L. J. Dixon and D. A. Kosower, Ann. Rev. Nucl. Part. Sci. 46
1996
Cited alongside, same era.
G. Chalmers and W. Siegel, Phys. Rev. D 59
1999
Cited alongside, same era.
J. M. Maldacena, Adv. Theor. Math. Phys. 2
1999
Cited alongside, same era.
Z. Bern, L. J. Dixon, M. Perelstein and J. S. Rozowsky, Nucl. Phys. B 546
1999
Cited alongside, same era.
N. Beisert, C. Kristjansen and M. Staudacher, Nucl. Phys. B 664
2003
Cited alongside, same era.
Z. Bern, L. J. Dixon, D. C. Dunbar and D. A. Kosower, Nucl. Phys. B 425
2004
Cited alongside, same era.
E. Witten, Commun. Math. Phys. 252
2004
Cited alongside, same era.
V.A. Smirnov, “Evaluating Feynman Integrals,” Springer Tracts in Modern Physics. Volume 211. Springer-Verlag 2004
2004
Cited alongside, same era.
F. Cachazo, P. Svrcek and E. Witten, JHEP 0409
2004
Cited alongside, same era.

Then

N. E. J. Bjerrum-Bohr, D. C. Dunbar, H. Ita, W. B. Perkins and K. Risager, JHEP 0612
2006
Later among the works it cites.
A. V. Kotikov, L. N. Lipatov, A. I. Onishchenko and V. N. Velizhanin, Phys. Lett. B 595
2006
Later among the works it cites.
R. Britto, B. Feng and P. Mastrolia, Phys. Rev. D 73
2006
Later among the works it cites.
For reviews, see e.g. M. L. Mangano and S. J. Parke, Phys. Rept. 200
Original
2007
Later among the works it cites.
For a recent review see e.g. Z. Bern, L. J. Dixon and D. A. Kosower, Annals Phys. 322
Original
2007
Later among the works it cites.
L. F. Alday and J. M. Maldacena, JHEP 0706
Original
2007
Later among the works it cites.
Z. Bern, J. J. Carrasco, L. J. Dixon, H. Johansson, D. A. Kosower and R. Roiban, Phys. Rev. Lett. 98
2007
Later among the works it cites.
Z. Bern, L. J. Dixon and R. Roiban, Phys. Lett. B 644
2007
Later among the works it cites.
M. B. Green, J. G. Russo and P. Vanhove, JHEP 0702
2007
Later among the works it cites.
M. B. Green, J. G. Russo and P. Vanhove, Phys. Rev. Lett. 98
2007
Later among the works it cites.
N. Berkovits, Phys. Rev. Lett. 98
2007
Later among the works it cites.
D. Forde, Phys. Rev. D 75
Original
2007
Later among the works it cites.
P. Mastrolia, Phys. Lett. B 644
2007
Later among the works it cites.
Z. Bern, J. J. M. Carrasco, H. Johansson and D. A. Kosower, Phys. Rev. D 76
Original
2007
Later among the works it cites.
M. B. Green, H. Ooguri and J. H. Schwarz, Phys. Rev. Lett. 99
Original
2007
Later among the works it cites.
For a recent discussion, see N. Arkani-Hamed, S. Dubovsky, A. Nicolis, E. Trincherini and G. Villadoro, JHEP 0705
Original
2007
Later among the works it cites.
R. Boels, L. Mason and D. Skinner, JHEP 0702
2007
Later among the works it cites.
N. Arkani-Hamed and J. Kaplan, JHEP 0804
Original
2008
Closest in time.
J. M. Drummond, G. P. Korchemsky and E. Sokatchev, Nucl. Phys. B 795
Original
2008
Closest in time.
G. Ossola, C. G. Papadopoulos and R. Pittau, Nucl. Phys. B 763
Original
2008
Closest in time.
R. Kallosh and M. Soroush, Nucl. Phys. B 801
Original
2008
Closest in time.

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