Ultraviolet Properties of N = 8 Supergravity at Five Loops

Abstract

We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of $N=8$ supergravity whose leading ultraviolet behavior we analyze using state of the art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is $D_c=24/5$, corresponding to a $D^8{R}^4$ counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional $N=4$ supergravity at three loops and $N=5$ supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard-symmetry considerations. We express this $D_c=24/5$ divergence in terms of two relatively simple positive-definite integrals reminiscent of vacuum integrals, excluding any additional ultraviolet cancellations at this loop-order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.

72 pages, 21 figures, RevTex

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