The action with manifest E7 type symmetry

Abstract

We generalize Cremmer-Julia 1st order action of N = 8 supergravity with manifest E 7(7) symmetry to cases of N = 6 with manifest SO * (12) and N = 5 with manifest SU (1, 5) duality symmetries. These U dualities belong to groups of type E7 which do not admit a symmetric bilinear invariant for vector fields. Therefore the 2d order classical action derived from the one with manifest E7 type duality has a ghost vector field which, under appropriate boundary conditions, decouples. We show that when classical N ≥ 5 supergravities are deformed by a candidate UV divergence the ghost field does not decouple. Therefore we argue that U duality and supersymmetry suggest an explanation of the mysterious cancellation of UV infinities at L = 4, N = 5 in d=4. The same reasoning implies that, in absence of duality and supersymmetry anomalies, which still require a better understanding, N ≥ 5 perturbative supergravities may be UV finite at higher-loops.1 For N ≤ 3 G-duality groups might be degenerate, when the quartic invariant degenerates into a perfect square. But these models have G-duality anomalies anyway, as shown in [12], and are not expected to be fully protected by G-duality against UV divergences.2 We discuss the current status of anomalies in supergravities in Appendix B. 3 N ≤ 4 supergravities interacting with matter are discussed in Appendix C.-2 -6 loop order, based on supersymmetry and E 7(7) symmetry. This explains the computations in [23,24] which have shown UV finiteness at 3 and 4 loops. But the prediction of [22] is still to be confirmed at 5 and 6 loops in N = 8 d=4. The analysis in [22], based on soft limit on scalars due to E 7(7) symmetry, is inconclusive starting from 7 loops.Meanwhile for N = 8 other arguments were given about all-loop finiteness based on the light-cone formalism [25]. It is interesting that the light-cone finiteness argument in [25] was not disputed, but the light-cone candidate counterterms at loop order L were not constructed either. Therefore they are not known to exists in N = 8 supergravity. A consistent supersymmetric reduction to N = 5, 6 was not studied so far.A different argument about finiteness of N = 8 supergravity is based on E 7(7) symmetry in the vector sector of the theory [14,15]. The E 7(7) symmetry argument in [14,15] was disputed by BN in [13], where a proposal was made that the E 7(7) symmetry can be restored even in presence of the candidate counterterms. The proposal is based on a construction of the source of deformation, defined in details in [26]. The source of deformation has a manifest E 7(7) symmetry, where instead of a physical vector in representation 28, 28 of SU (8) one has to use a symplectic doublet with twice as many vector fields. An improved version of this proposal for U (1) duality group was developed in [26] and it was applied to the Born-Infeld theory, as well as Born-Infeld theory with higher derivatives [27,28]. The proof of consistency of the deformation proposal in bosonic theory was given in [13] only at a base point of the moduli space, whe...

The Duality Between Color and Kinematics and its Applications

“…See, however, Refs. [318,319] for arguments suggesting that U-duality invariance may be ultimately responsible. It is of considerable interest to settle the origin of these cancellations, and to know whether they continue to higher orders.…”

CMB targets after the latest Planck data release

“…Two red lines show predictions of the simplest E models. Two purple lines are for the quartic KKLTI model (66), two magenta lines show the predictions of the model (70). The set of these simple q ¼ 2 and q ¼ 5=2 attractors completely covers the sweet spot of the Planck 2018 data.…”

“…This U-duality symmetry together with maximal supersymmetry is believed to be the reason why in perturbative N ¼ 8 supergravity the UV properties are better than expected naively, and N > 4 supergravities may be even UV finite, if U-duality symmetry has no anomalies; see, for example,[65][66][67].…”

M-theory, black holes and cosmology

“…They have shown that maximal supergravity behaves in UV much better than expected. It was suggested in [38][39][40] that E 7(7) symmetry together with the maximal supersymmetry of perturbative maximal supergravity in 4d might explain the cancellation of UV infinities observed in 'theoretical experiments' as described in [37]. It would be very interesting to learn more about these exceptional symmetries and their role in physics.…”