Stringy KLT relations, global symmetries, and E7(7)-violation

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 e(-6 phi)R(4) 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 e(-6 phi)R(4). This allows us to extract the matrix elements of the unique SU(8)-invariant supersymmetrization of R-4. Their single-soft scalar limits are non-vanishing. This demonstrates that the N = 8 supergravity candidate counterterm R-4 is incompatible with continuous E-7(7) symmetry. From the soft scalar limits, we reconstruct to quadratic order the SU(8)-invariant function of scalars that multiplies R-4, and show that it satisfies the Laplace eigenvalue equation derived recently from supersymmetry and duality constraints.