Eisenstein series for higher-rank groups and string theory amplitudes - High Energy Physics - TheoryReport as inadecuate




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Abstract: Scattering amplitudes of superstring theory are strongly constrained by therequirement that they be invariant under dualities generated by discretesubgroups, E nZ, of simply-laced Lie groups in the E n series n<= 8. Inparticular, expanding the four-supergraviton amplitude at low energy gives aseries of higher derivative corrections to Einstein-s theory, with coefficientsthat are automorphic functions with a rich dependence on the moduli. Boundaryconditions supplied by string and supergravity perturbation theory, togetherwith a chain of relations between successive groups in the E n series,constrain the constant terms of these coefficients in three distinct parabolicsubgroups. Using this information we are able to determine the expressions forthe first two higher derivative interactions which are BPS-protected in termsof specific Eisenstein series. Further, we determine key features of thecoefficient of the third term in the low energy expansion of thefour-supergraviton amplitude which is also BPS-protected in the E 8 case.This is an automorphic function that satisfies an inhomogeneous Laplaceequation and has constant terms in certain parabolic subgroups that containinformation about all the preceding terms.



Author: Michael B. Green, Stephen D. Miller, Jorge G. Russo, Pierre Vanhove

Source: https://arxiv.org/







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