Abstract
The role of duality symmetries in the construction of counterterms for maximal supergravity theories is discussed in a field-theoretic context from different points of view. These are: dimensional reduction, the question of whether appropriate superspace measures exist and information about non-linear invariants that can be gleaned from linearised ones. The former allows us to prove that F-term counterterms cannot be E-7(7)-invariant in D = 4, N = 8 supergravity or E-6(6)-invariant in D = 5 maximal supergravity. This is confirmed by the two other methods which can also be applied to D = 4 theories with fewer supersymmetries and allow us to prove that N = 6 supergravity is finite at three and four loops and that N = 5 supergravity is three-loop finite.
| Original language | English |
|---|---|
| Article number | 020 |
| Journal | Journal of High Energy Physics |
| Volume | 2011 |
| Issue number | 1 |
| Publication status | Published - 2011 |