$R^4$ couplings and automorphic unipotent representations - High Energy Physics - TheoryReport as inadecuate

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Abstract: Four-graviton, eight-derivative couplings in the low energy effective actionof toroidal type II string compactifications are tightly constrained byU-duality invariance and by supersymmetry. In this note, we revisit earlierproposals for the automorphic form governing these couplings in dimensionD=3,4,5,6, and propose that the correct automorphic form is the minimal thetaseries for the corresponding U-duality group. Evidence for this proposal comesfrom i the matching of infinitesimal characters, ii the fact that the Fouriercoefficients have support on 1-2-BPS charges and iii decompactificationlimits. In particular, we show that non-perturbative effects can be interpretedas 1-2-BPS instantons, or 1-2-BPS particles in one dimension higher togetherwith Taub-NUT instantons in the D=3 case. Based on similar considerations, wealso conjecture the form of 1-4-BPS saturated couplings such as $ abla^4 R^4$couplings in the same dimensions.

Author: Boris Pioline LPTHE

Source: https://arxiv.org/

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