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Integral invariants in 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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Stelle,  K. S.
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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JHEP2011_05_021.pdf
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Citation

Bossard, G., Howe, P., Lindstrom, U., Stelle, K. S., & Wulff, L. (2011). Integral invariants in maximally supersymmetric Yang-Mills theories. Journal of High Energy Physics, 2011(05): 021. doi:10.1007/JHEP05(2011)021.


Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-C945-3
Abstract
Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions 4 ≤ D ≤ 10 for SU(k) gauge groups. It is shown that, in addition to the action, there are three special invariants in all dimensions. Two of these, the single-and double-trace F 4 invariants, are of Chern-Simons type in D = 9, 10 and BPS type in D ≤ 8, while the third, the double-trace of two derivatives acting on F 4, can be expressed in terms of a gauge-invariant super-D -form in all dimensions. We show that the super-ten-forms for D = 10 F 4 invariants have interesting cohomological properties and we also discuss some features of other invariants, including the single-trace d 2 F 4, which has a special form in D = 10. The implications of these results for ultra-violet divergences are discussed in the framework of algebraic renormalisation.