5 loops in 24/5 dimensions
Jonas Bjornsson, Michael B. Green

TL;DR
This paper investigates the ultraviolet divergences of maximally supersymmetric field theories using a pure spinor particle approach, revealing a potential five-loop divergence in 24/5 dimensions and implications for supergravity's divergence protection.
Contribution
It introduces a first quantised pure spinor particle method to systematically analyze loop amplitudes and divergences in supersymmetric theories, uncovering new divergence patterns at five loops.
Findings
Identifies momentum factors multiplying R^4 in supergravity and F^4 in Yang-Mills.
Shows leading divergences at 2-4 loops align with previous field theory results.
Predicts a five-loop divergence at 24/5 dimensions and suggests all loops contribute to certain divergences.
Abstract
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…
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Taxonomy
TopicsMathematics and Applications · graph theory and CDMA systems
