Stringy KLT relations, global symmetries, and E_7(7) violation

TL;DR

This paper investigates how string theory amplitudes relate to supergravity symmetries, revealing that certain counterterms violate the E7(7) symmetry, with implications for understanding quantum gravity divergences.

Contribution

It provides explicit superamplitudes for SU(4)xSU(4)-symmetric operators, analyzes SU(8)-violating amplitudes, and demonstrates the incompatibility of R^4 counterterms with E7(7) symmetry in N=8 supergravity.

Findings

SU(8)-violating amplitudes classified and explicitly derived.

SU(8)-invariant R^4 matrix elements extracted from string amplitudes.

Non-vanishing soft scalar limits show R^4 counterterm breaks E7(7) symmetry.

Abstract

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) 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 exp(-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.