2010/07/31 by Henriette Elvang, Michael Kiermaier
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Invariant (physics) #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Quantum Chromodynamics and Particle Interactions #Scalar (mathematics) #String theory #Supergravity #Supersymmetry #hep-th
paper · pdf · doi:10.1007/jhep10(2010)108
published as JHEP 1010:108,2010 · 23 pages, published version
openalex publication_date 2010/10/01 · arxiv created 2010/10/28 · arxiv updated 2010/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study consequences of the Kawai-Lewellen-Tye (KLT) relations applied to tree amplitudes in toroidal compactifications of string theory to four dimensions. The closed string tree amplitudes with massless external states respect a global SU(4)xSU(4) symmetry, which is enhanced to the SU(8) R-symmetry of N=8 supergravity in the field theory limit. Our analysis focuses on two aspects: (i) We provide a detailed account of the simplest SU(8)-violating amplitudes. We classify these processes and derive explicit superamplitudes for all local 5- and 6-point operators with SU(4)xSU(4) symmetry at order alpha'3. Their origin is the dilatonic operator exp(-6 phi) R4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order alpha'3 and use two different methods to isolate the SU(8)-singlet contribution from exp(-6 phi) R4. This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N=8 supergravity candidate counterterm R4 is incompatible with continuous E7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.