2015/02/28 by Boris Pioline · 2 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Duality (order theory) #Effective action #Eisenstein series #Graviton #Group (periodic table) #M-theory #Mathematical physics #Mathematics #Modular form #Particle physics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum gravity #Quantum mechanics #Relationship between string theory and quantum field theory #S-duality #String (physics) #String duality #String theory #Supergravity #Supersymmetry #Theoretical physics #Torus #hep-th
paper · pdf · doi:10.1007/jhep04(2015)057
18 pages (+ 26 page appendix), three Mathematica files included with submission; v2: minor corrections, version to appear in JHEP
openalex publication_date 2015/04/01 · arxiv created 2015/04/15 · arxiv updated 2015/06/23 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Four-graviton couplings in the low energy effective action of type II string vacua compactified on tori are strongly constrained by supersymmetry and U-duality. While the ℛ4 and D4ℛ4 couplings are known exactly in terms of Langlands-Eisenstein series of the U-duality group, the D6ℛ4 couplings are not nearly as well understood. Exploiting the coincidence of the U-duality group in D = 6 with the T-duality group in D = 5, we propose an exact formula for the D6ℛ4 couplings in type II string theory compactified on T4, in terms of a genus-two modular integral plus a suitable Eisenstein series. The same modular integral computes the two-loop correction to D6ℛ4 in 5 dimensions, but here provides the non-perturbative completion of the known perturbative terms in D = 6. This proposal hinges on a systematic re-analysis of the weak coupling and large radius of the D6ℛ4 in all dimensions D ≥ 3, which fills in some gaps and resolves some inconsistencies in earlier studies.