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

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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) × SU(4) symmetry, which is enhanced to the SU(8) R -symmetry of \( \mathcal{N} = 8 \) 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) × SU(4) symmetry at order α′3 . Their origin is the dilatonic operator e−6φ R 4 in the closed-string effective action. (ii) We expand the 6-point closed string tree amplitudes to order α3 and use two different methods to isolate the SU(8)-singlet contribution from e−6φ 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 \( \mathcal{N} = 8 \) 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.

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Authors and Affiliations

  1. Michigan Center for Theoretical Physics (MCTP), Department of Physics, University of Michigan, 450 Church St, Ann Arbor, MI, 48109, U.S.A.

    Henriette Elvang

  2. School of Natural Sciences, Institute for Advanced Study, Einstein Drive, Princeton, NJ, 08540, U.S.A.

    Henriette Elvang

  3. Department of Physics, Princeton University, Princeton, NJ, 08544, U.S.A.

    Michael Kiermaier

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  1. Henriette Elvang
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  2. Michael Kiermaier
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Correspondence to Henriette Elvang.

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ArXiv ePrint : 1007.4813

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Elvang, H., Kiermaier, M. Stringy KLT relations, global symmetries, and E 7(7)-violation. J. High Energ. Phys. 2010, 108 (2010). https://doi.org/10.1007/JHEP10(2010)108

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