5 loops in 24/5 dimensions

Details 5 loops in 24/5 dimensions 5 loops in 24/5 dimensions

2010-04-15

arxiv.org/abs/1004.2692v4

JHEP 1008:132,2010

Physics

High Energy Physics

High Energy Physics - Theory

23 pages, 7 figures. Version published in journal

Scientific paper

10.1007/JHEP08(2010)132

A first quantised approach to loop amplitudes based on the pure spinor particle is applied to the systematics of four-particle amplitudes in maximally supersymmetric field theories. Counting of fermionic zero modes allows the identification of momentum factors multiplying R**4 in the case of supergravity (and F**4 in the Yang--Mills case) thereby making manifest their ultraviolet properties as a function of dimension, D. For L=2,3,4 loops the leading supergravity divergence is in D=4+6/L dimensions and proportional to d*2L R**4, in line with earlier field theory calculations. However, at five loops there is a radical change in the systematics, suggesting the presence of a contribution with an explicit L=5 logarithmic ultraviolet divergence when D=24/5 that is proportional to d*8 R**4. We further argue that d*8 R**4 should receive contributions from all loops, which would imply that N=8 supergravity (with D=4) is not protected by supersymmetry from a seven-loop divergence.

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