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تسجيل مستخدم جديد$R^4$ couplings and automorphic unipotent representations
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تأليف
Boris Pioline
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Four-graviton, eight-derivative couplings in the low energy effective action of toroidal type II string compactifications are tightly constrained by U-duality invariance and by supersymmetry. In this note, we revisit earlier proposals for the automorphic form governing these couplings in dimension D=3,4,5,6, and propose that the correct automorphic form is the minimal theta series for the corresponding U-duality group. Evidence for this proposal comes from i) the matching of infinitesimal characters, ii) the fact that the Fourier coefficients have support on 1/2-BPS charges and iii) decompactification limits. In particular, we show that non-perturbative effects can be interpreted as 1/2-BPS instantons, or 1/2-BPS particles in one dimension higher (together with Taub-NUT instantons in the D=3 case). Based on similar considerations, we also conjecture the form of 1/4-BPS saturated couplings such as $ abla^4 R^4$ couplings in the same dimensions.
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Unlike the $mathcal{R}^4$ and $ abla^4mathcal{R}^4$ couplings, whose coefficients are Langlands-Eisenstein series of the U-duality group, the coefficient $mathcal{E}_{(0,1)}^{(d)}$ of the $ abla^6mathcal{R}^4$ interaction in the low-energy effective
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