TY - JOUR

T1 - Duality Constraints on Counterterms in N=5,6 Supergravities

AU - Freedman, Daniel Z.

AU - Kallosh, Renata

AU - Yamada, Yusuke

N1 - Funding Information:
We are grateful to Z. Bern, L. Dixon, and especially to H. Elvang for useful discussions of the current work and to H. Nicolai and R. Roiban for a collaboration on a related project. This work is supported by SITP and by the US National Science Foundation grant PHY-1720397. The work of DZF is partially supported by US NSF grant Phy-1620045.
Publisher Copyright:
© 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

PY - 2018/10

Y1 - 2018/10

N2 - The UV finiteness found in calculations of the 4-point amplitude in N = 5 supergravity at loop order L = 3, 4 has not been explained, which motivates our study of the relevant superspace invariants and on-shell superamplitudes for both N = 5 and N = 6. The local 4-point superinvariants for L = 3,4 are expected to have nonlinear completions whose 6-point amplitudes have non-vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For N = 5, we find at L = 3 that local 6-point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4-point counterterm and thus gives a plausible explanation of the observed L = 3 finiteness. However, at L = 4 we construct a local 6-point superinvariant with non-vanishing SSL's, so the SSL argument does not explain the observed L = 4 N = 5 UV finiteness. For N = 6 supergravity there are no 6-point invariants at either L = 3 or 4, so the SSL argument predicts UV finiteness.

AB - The UV finiteness found in calculations of the 4-point amplitude in N = 5 supergravity at loop order L = 3, 4 has not been explained, which motivates our study of the relevant superspace invariants and on-shell superamplitudes for both N = 5 and N = 6. The local 4-point superinvariants for L = 3,4 are expected to have nonlinear completions whose 6-point amplitudes have non-vanishing SSL's (soft scalar limits), violating the behavior required of Goldstone bosons. For N = 5, we find at L = 3 that local 6-point superinvariant and superamplitudes, which might cancel these SSL's, do not exist. This rules out the candidate 4-point counterterm and thus gives a plausible explanation of the observed L = 3 finiteness. However, at L = 4 we construct a local 6-point superinvariant with non-vanishing SSL's, so the SSL argument does not explain the observed L = 4 N = 5 UV finiteness. For N = 6 supergravity there are no 6-point invariants at either L = 3 or 4, so the SSL argument predicts UV finiteness.

KW - duality constraints

KW - supergravity

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U2 - 10.1002/prop.201800054

DO - 10.1002/prop.201800054

M3 - Article

AN - SCOPUS:85053811504

SN - 0015-8208

VL - 66

JO - Fortschritte der Physik

JF - Fortschritte der Physik

IS - 10

M1 - 1800054

ER -