A note on the UV behaviour of maximally supersymmetric Yang–Mills theories

2009/08/31 by Guillaume Bossard, G. Bossard, P. S. Howe +3 · 1 citation
Physics and Astronomy · #Black Holes and Theoretical Physics #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions #hep-th

paper · pdf · doi:10.1016/j.physletb.2009.10.084

published as Phys.Lett.B682:137-142,2009 · 12 pages. Minor changes to text. References added

arxiv created 2009/10/05 · openalex publication_date 2009/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

The question of whether BPS invariants are protected in maximally supersymmetric Yang-Mills theories is investigated from the point of view of algebraic renormalisation theory. The protected invariants are those whose cohomology type differs from that of the action. It is confirmed that one-half BPS invariants (F⁴) are indeed protected while the double-trace one-quarter BPS invariant (d²F⁴) is not protected at two loops in D=7, but is protected at three loops in D=6 in agreement with recent calculations. Non-BPS invariants, i.e. full superspace integrals, are also shown to be unprotected.

Citations

• ICTP Lectures on Covariant Quantization of the Superstring
• The ultra-violet question in maximally supersymmetric field theories
• Partial non-renormalisation of the stress-tensor four-point function in N=4 SYM and AdS/CFT
• One-Loop n-Point Gauge Theory Amplitudes, Unitarity and Collinear Limits
• Local BRST cohomology in the antifield formalism: I. General theorems
• Shadow fields and local supersymmetric gauges

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