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Eisenstein series for higher-rank groups and string theory amplitudes
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In this paper, it was shown that a chain of relations between successive groups in the E_n series, together with the constant terms of these coefficients in three distinct parabolic subgroups, can be used to determine the expressions for the first two higher derivative interactions in terms of specific Eisenstein series.Abstract:
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. Further, we determine key features of the coefficient of the third term in the low energy expansion of the four-supergraviton amplitude (which is also BPS-protected) in the E_8 case. This is an automorphic function that satisfies an inhomogeneous Laplace equation and has constant terms in certain parabolic subgroups that contain information about all the preceding terms.read more
Citations
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Differential geometry with a projection: Application to double field theory
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E7(7) constraints on counterterms in N=8 supergravity
Niklas Beisert,Henriette Elvang,Henriette Elvang,Daniel Z. Freedman,Michael Kiermaier,Alejandro H. Morales,Stephan Stieberger +6 more
TL;DR: In this article, it was shown that the 6-point matrix elements of D 4 R 4 and D 6 R 4 in N = 8 supergravity have non-vanishing single-soft scalar limits, and therefore these operators violate the continuous E 7 ( 7 ) symmetry.
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String theory dualities and supergravity divergences
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On the modular structure of the genus-one Type II superstring low energy expansion
TL;DR: In this paper, it was shown that a certain class of modular functions satisfy Laplace eigenvalue equations with inhomogeneous terms that are polynomial in non-holomorphic Eisenstein series.
References
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Unity of superstring dualities
Chris Hull,Paul K. Townsend +1 more
TL;DR: In this article, it was shown that the effective action for type II string theory compactified on a six-torus is N = 8 supergravity, which is known to have an E7 duality symmetry.
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One loop in eleven dimensions
TL;DR: In this article, the four-graviton scattering in eleven-dimensional supergravity is considered at one loop compactified on one, two and three-dimensional tori, and the dependence on the toroidal geometry determines the known perturbative and nonperturbative terms in the corresponding processes in type II superstring theories in ten, nine and eight dimensions.
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Supersymmetry constraints on type IIB supergravity
Michael B. Green,Savdeep Sethi +1 more
TL;DR: In this paper, it was shown that certain modular invariant interactions relative to the Einstein-Hilbert term are proportional to eigenfunctions of the Laplace operator on the fundamental domain of SL(2,Z).
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