Duality Constraints on Counterterms in $\mathcal{N}=5,6$ Supergravities

Abstract

The UV finiteness found in calculations of the 4-point amplitude in $\mathcal{N}=5$ 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 $\mathcal{N}=5$ and $\mathcal{N}=6$. 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 $\mathcal{N}=5$, 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 $L=4$ $\mathcal{N}=5$ UV finiteness. For $\mathcal{N}=6$ supergravity there are no 6-point invariants at either $L=3$ or 4, so the SSL argument predicts UV finiteness.

28 pages, v2: references added, v3: typos corrected

References in corpus (7)

• Three-Loop Superfiniteness of N=8 Supergravity
• Generating Tree Amplitudes in N=4 SYM and N=8 SG
• E7(7) constraints on counterterms in N=8 supergravity
• Stringy KLT relations, global symmetries, and E_7(7) violation
• Explicit Action of E7(7) on N=8 Supergravity Fields
• N=8 Supergravity 4-point Amplitudes
• The D^{2k} R^4 Invariants of N=8 Supergravity

Cited by in corpus (7)

• Double Copy from Homotopy Algebras
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Supersymmetry constraints on U-duality invariant deformations of $N\ge 5$ Supergravity
• The Action with Manifest E7 Type Symmetry
• Two-loop n-point anomalous amplitudes in N=4 supergravity
• Asymptotic safety and quantum gravity amplitudes
• Deformation of d=4, N> 4 Supergravities Breaks Nonlinear Local Supersymmetry