Integral invariants in maximally supersymmetric Yang-Mills theories

Abstract

Integral invariants in maximally supersymmetric Yang-Mills theories are discussed in spacetime dimensions $4\le D\le 10$ 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 $D\le 8$, 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.

20 pages, 1 table

References in corpus (2)

• 5 loops in 24/5 dimensions
• The ultra-violet question in maximally supersymmetric field theories

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