Revision 2

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Changes against revision 1:

Title · changed: Revision 1: Is four-dimensional $N=8$ supergravity ultraviolet finite at seven loops; Revision 2: Is four-dimensional $N=8$ supergravity ultraviolet finite at seven loops?
Plain: $N=8$ supergravity is the most symmetric theory of gravity in four dimensions and might lack the infinities that ruin ordinary quantum gravity. Known symmetries first allow an infinity at seven loops, a calculation not yet done.
Precise: Compute the coefficient of the seven-loop logarithmic ultraviolet divergence (the $D^{8}R^{4}$ counterterm) of the four-graviton amplitude in $D=4$ $N=8$ supergravity, or prove it vanishes. The highest computed order gives critical dimension $D_{c}=24/5$ at five loops (Bern et al., Phys. Rev. D 98, 086021, 2018).
Settled by: Construction of the seven-loop four-graviton integrand and extraction of its $D = 4$ ultraviolet divergence, or a symmetry argument forbidding the counterterm.
Kind: well-posed
Answer type: yes-no
References: (empty)
Literature status: open
Status note: No six- or seven-loop result reported as of 2026.
Posed since: 2006

Decisions