New \(E_{7(7)}\) invariants and amplitudes. (English) Zbl 1397.83040
Summary: We construct a new class of manifest \(E_{7(7)}\) duality invariants, which generalize the Cartan quartic invariant, familiar from studies of the black hole entropy. The new ones, being four-linear, are designed for studies of the four-vector amplitudes and to be used, upon supersymmetrization, as initial sources of deformation for the non-linear higher-derivative generalizations of the linear twisted self-duality condition. We show, however, that the new invariants are inconsistent with the expected UV divergent amplitudes in extended supergravities with non-degenerate duality groups of type \(E7\). When \(E_{7(7)}\) degenerates into \(U(1)\) the new invariants reproduce the recently discovered source of deformation for the Born-Infeld duality invariant model with higher derivatives relevant to UV divergences of the D3 brane action. These facts may explain the UV properties of perturbative supergravity.
MSC:
| 83C47 | Methods of quantum field theory in general relativity and gravitational theory |
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