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

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.

23 pages, published version

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Cited by in corpus (14)

• The Momentum Kernel of Gauge and Gravity Theories
• E7(7) constraints on counterterms in N=8 supergravity
• On-shell constructibility of tree amplitudes in general field theories
• On duality symmetries of supergravity invariants
• E7(7) symmetry in perturbatively quantised N=8 supergravity
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• N=8 Counterterms and E7(7) Current Conservation
• Complete N-Point Superstring Disk Amplitude II. Amplitude and Hypergeometric Function Structure
• The Ultraviolet Finiteness of N=8 Supergravity
• The D^{2k} R^4 Invariants of N=8 Supergravity
• On tree amplitudes with gluons coupled to gravitons
• A note on N=8 counterterms
• On KLT and SYM-supergravity relations from 5-point 1-loop amplitudes
• Perturbative Gravity and Gauge Theory Relations -- A Review