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CSW-like Expansion for Einstein Gravity · Around

2012

CSW-like Expansion for Einstein Gravity

Penante, Brenda, Rajabi, Sayeh, Sizov, Grigory

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Using the recent formula presented by He and Cachazo-Mason-Skinner for the link representation of tree-level N=8 supergravity amplitudes, we derived a CSW-like expansion for the Next-to-MHV 6- and 7-graviton amplitudes by using the global residue theorem; a technique introduced originally for Yang-Mills amplitudes.

We analytically checked the equivalence of one of the CSW terms and its corresponding Risager's diagram.
For the remaining 6-graviton and all 7-graviton terms, we numerically checked the agreement with Risager's expansion.
We showed that the conditions for the absence of contributions at infinity of the global residue theorem are satisfied for any number of particles.

Built on

A. Hodges, “A simple formula for gravitational MHV amplitudes,” arXiv:1204.1930 [hep-th]
Original
1930
Earlier work this paper cites.
F. Cachazo, P. Svrcek, and E. Witten, “MHV vertices and tree amplitudes in gauge theory,” JHEP
2004
Earlier work this paper cites.
E. Witten, “Perturbative gauge theory as a string theory in twistor space,” Commun.Math.Phys
2004
Earlier work this paper cites.
R. Roiban, M. Spradlin, and A. Volovich, “On the tree level S matrix of Yang-Mills theory,” Phys.Rev
2004
Earlier work this paper cites.
K. Risager, “A Direct proof of the CSW rules,” JHEP
2005
Earlier work this paper cites.

Similar

R. Britto, F. Cachazo, and B. Feng, “New recursion relations for tree amplitudes of gluons,” Nucl.Phys
2005
Cited alongside, same era.
R. Britto, F. Cachazo, B. Feng, and E. Witten, “Direct proof of tree-level recursion relation in Yang-Mills theory,” Phys.Rev.Lett
2005
Cited alongside, same era.
P. Benincasa, C. Boucher-Veronneau, and F. Cachazo, “Taming Tree Amplitudes In General Relativity,” JHEP
2007
Cited alongside, same era.
M. Bianchi, H. Elvang, and D. Z. Freedman, “Generating Tree Amplitudes in N=4 SYM and N = 8 SG,” JHEP
Original
2008
Cited alongside, same era.
N. Arkani-Hamed and J. Kaplan, “On Tree Amplitudes in Gauge Theory and Gravity,” JHEP
Original
2008
Cited alongside, same era.
S. He, “A Link Representation for Gravity Amplitudes,” arXiv:1207.4064 [hep-th]
Original
Cited in the paper.
F. Cachazo, L. Mason, and D. Skinner, “Gravity in Twistor Space and its Grassmannian Formulation,” arXiv:1207.4712 [hep-th]
Original
Cited in the paper.
F. Cachazo and D. Skinner, “Gravity from Rational Curves,” arXiv:1207.0741 [hep-th]
Original
Cited in the paper.
M. Bullimore, “New Formulae for Gravity Amplitudes: Parity Invariance and Soft Limits,” arXiv:1207.3940 [hep-th]
Original
Cited in the paper.

Then

N. Arkani-Hamed, F. Cachazo, C. Cheung, and J. Kaplan, “A Duality For The S Matrix,” JHEP
Original
2010
Later among the works it cites.
N. Arkani-Hamed, J. Bourjaily, F. Cachazo, and J. Trnka, “Local Spacetime Physics from the Grassmannian,” JHEP
Original
2011
Later among the works it cites.
Wiley Classics Library Wiley Classics Library. Wiley, 2011
P. Griffiths and J. Harris, Principles of Algebraic Geometry · 2011
Later among the works it cites.
E. Conde and S. Rajabi, “The Anomaly of the Twelve-Graviton Next-to-MHV Risager Amplitude,” JHEP
Original
2012
Closest in time.

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