5 loops in 24/5 dimensions

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 supergravity (with D=4) is not protected by supersymmetry from a seven-loop divergence.

23 pages, 7 figures. Version published in journal

References in corpus (7)

• Three-Loop Superfiniteness of N=8 Supergravity
• Ultraviolet properties of Maximal Supergravity
• New Higher-Derivative $R^4$ Theorems
• Multiloop Superstring Amplitudes from Non-Minimal Pure Spinor Formalism
• Pure Spinor Vertex Operators in Siegel Gauge and Loop Amplitude Regularization
• Worldline Green Functions for Arbitrary Feynman Diagrams
• Higher-loop amplitudes in the non-minimal pure spinor formalism

Cited by in corpus (8)

• On D=5 super Yang-Mills theory and (2,0) theory
• The Complete Four-Loop Four-Point Amplitude in N=4 Super-Yang-Mills Theory
• On duality symmetries of supergravity invariants
• Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
• The Ultraviolet Finiteness of N=8 Supergravity
• The D^{2k} R^4 Invariants of N=8 Supergravity
• Pure Spinor Integration from the Collating Formula
• Maximally Supersymmetric Yang-Mills in five dimensions in light-cone superspace