High Energy Theory Seminar

N=8 supergravity is not renormalizable. This means the presense of power divergences in the amplitudes. There are also logarithmic divergences that multiply higher-dimensional counterterms. In all probability, the latter appear starting from the 7-th or maybe from the 8-th loop. Supergravity is extremely complicated, and it makes sense to study simpler theories that exhibit the same properties. The N=(1,1) supersymmetric Yang-Mills (SYM) theory in six dimensions represents such a toy model. Nontrivial counterterms and the associated logarithmic ultraviolet divergences in the amplitudes arise there already at the 3-d loop level.

After making some general comments on the structure of nonrenormalizable supersymmetric theories, we will revisit the issue of higher-dimensional counterterms for N=(1,1) 6D SYM using the off-shell N=(1,0) and on-shell N=(1,1) harmonic superspace approaches. The second approach is developed in full generality and used to solve, for the first time, the N=(1,1) SYM constraints in terms of N=(1,0) superfields. This provides a convenient tool to write explicit expressions for the candidate counterterms and other N=(1,1) invariants and may be conducive to proving non-renormalization theorems needed to explain the absence of certain logarithmic divergences in higher-loop contributions to scattering amplitudes in N=(1,1) SYM.