2010

Eisenstein series for higher-rank groups and string theory amplitudes

Green, Michael B., Miller, Stephen D., Russo, Jorge G. et al.

Understand

Scattering amplitudes of superstring theory are strongly constrained by the requirement that they be invariant under dualities generated by discrete subgroups, E_n(Z), of simply-laced Lie groups in the E_n series (n<= 8).

In particular, expanding the four-supergraviton amplitude at low energy gives a series of higher derivative corrections to Einstein's theory, with coefficients that are automorphic functions with a rich dependence on the moduli.
Boundary conditions supplied by string and supergravity perturbation theory, together with a chain of relations between successive groups in the E_n series, constrain the constant terms of these coefficients in three distinct parabolic subgroups.
Using this information we are able to determine the expressions for the first two higher derivative interactions (which are BPS-protected) in terms of specific Eisenstein series.

Built on

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Similar

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1997
Cited alongside, same era.
J. G. Russo and A. A. Tseytlin, “One-Loop Four-Graviton Amplitude in Eleven-Dimensional Supergravity,” Nucl. Phys. B 508
1997
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1997
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D. Ginzburg, S. Rallis, and D. Soudry, “On the automorphic theta representation for simply laced groups,” Israel J. Math. 100 (1997) 61-116
1997
Cited alongside, same era.
M. B. Green and M. Gutperle, “D-Instanton Partition Functions,” Phys. Rev. D 58
1998
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M. B. Green and S. Sethi, “Supersymmetry constraints on type IIB supergravity,” Phys. Rev. D 59
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Cited alongside, same era.
N. A. Obers and B. Pioline, “Eisenstein Series and String Thresholds,” Commun. Math. Phys. 209
2000
Cited alongside, same era.
S. Mizoguchi and G. Schroder, “On Discrete U-Duality in M-Theory,” Class. Quant. Grav. 17
2000
Cited alongside, same era.
M. B. Green and P. Vanhove, “The Low Energy Expansion of the One-Loop Type II Superstring Amplitude,” Phys. Rev. D 61
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Cited alongside, same era.
M. B. Green, H. h. Kwon and P. Vanhove, “Two Loops in Eleven Dimensions,” Phys. Rev. D 61
2000
Cited alongside, same era.
M. B. Green, J. G. Russo and P. Vanhove, “Automorphic properties of low energy string amplitudes in various dimensions”, arXiv:1001.2535 [hep-th]
Original
Cited in the paper.
M. B. Green, J. G. Russo and P. Vanhove, “String theory dualities and supergravity divergences”, arXiv:1002.3805 [hep-th]
Original
Cited in the paper.

Then

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2000
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2001
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2001
Later among the works it cites.
M. B. Green and P. Vanhove, “Duality and Higher Derivative Terms in M Theory,” JHEP 0601
2006
Later among the works it cites.
M. B. Green, J. G. Russo and P. Vanhove, “Non-renormalisation conditions in type II string theory and maximal supergravity,” JHEP 0702
2007
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A. Basu, “The D 4 R 4 Term in Type IIB String Theory on T 2 and U-Duality,” Phys. Rev. D 77
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2008
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Original
2008
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M. B. Green, J. G. Russo and P. Vanhove, “Modular properties of two-loop maximal supergravity and connections with string theory,” JHEP 0807
Original
2008
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C. Moeglin and J. L. Waldspurger, Spectral Decomposition and Eisenstein Series: A Paraphrase of the Scriptures
2008
Later among the works it cites.
M. B. Green, J. G. Russo and P. Vanhove, “Low energy expansion of the four-particle genus-one amplitude in type II superstring theory,” JHEP 0802
Original
2008
Later among the works it cites.

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