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

Bossard, Guillaume; Howe, P. S.; Stelle, K. S.

doi:http://dx.doi.org/10.1016/j.physletb.2009.10.084

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

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Bossard, Guillaume
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Bossard, G., Howe, P. S., & Stelle, K. S. (2009). A note on the UV behaviour of maximally supersymmetric Yang-Mills theories. Physics Letters B, 682(1), 137-142. doi: http://dx.doi.org/10.1016/j.physletb.2009.10.084.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0013-60D7-B

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 ($F^4$) are indeed protected while the double-trace one-quarter BPS invariant ($d^2F^4$) 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.