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Integral invariants in maximally supersymmetric Yang-Mills theories

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.

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Correspondence to P. S. Howe.

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ArXiv ePrint:1012.3142

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Bossard, G., Howe, P.S., Lindström, U. et al. Integral invariants in maximally supersymmetric Yang-Mills theories. J. High Energ. Phys. 2011, 21 (2011). https://doi.org/10.1007/JHEP05(2011)021

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Keywords

  • Extended Supersymmetry
  • Superspaces
  • Gauge Symmetry
  • Field Theories in Higher Dimensions