\(N=8\) counterterms and \(E_{7(7)}\) current conservation. (English) Zbl 1298.81351
Summary: We examine conservation of the \(E_{7(7)}\) Noether-Gaillard-Zumino current in the presence of N=8 supergravity counterterms using the momentum space helicity formalism, which significantly simplifies the calculations. The main result is that the 4-point counterterms at any loop order \(L\) are forbidden by the \(E_{7(7)}\) current conservation identity. We also clarify the relation between linearized and full non-linear superinvariants as candidate counterterms. This enables us to show that all \(n\)-point counterterms at \(L = 7, 8\) are forbidden since they provide a non-linear completions of the 4-point ones. This supports and exemplifies our general proof in [the author, “\(E_{7(7)}\) symmetry and finiteness of \(N=8\) supergravity”, arXiv:1103.4115] of perturbative UV finiteness of \(N=8\) supergravity.
MSC:
| 81T60 | Supersymmetric field theories in quantum mechanics |
| 83E50 | Supergravity |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81T18 | Feynman diagrams |
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