2010/01/31 by Boris Pioline · 2 citations
Mathematics · Physics and Astronomy · #Automorphic form #Black Holes and Theoretical Physics #Conjecture #Cosmology and Gravitation Theories #Dimension (graph theory) #Duality (order theory) #Effective action #Equivariant map #Graviton #Group (periodic table) #Instanton #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum mechanics #String (physics) #Theoretical physics #hep-th
paper · pdf · doi:10.1007/jhep03(2010)116
published as JHEP 1003:116,2010 · 30 pages; v2: new appendix on decompactification limits, and minor corrections, published version; v3: fixed various misprints
openalex publication_date 2010/03/01 · arxiv created 2014/06/20 · arxiv updated 2014/06/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31
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 ∇4 R 4 couplings in the same dimensions.