Orbifolding the N=4 SYM theory naively breaks its SU(4) R-symmetry group to a much smaller subgroup, such as SU(2)xU(1) if N=2 supersymmetry is preserved. I will discuss how, by extending our notion of symmetry to include Lie groupoids and their twists, one can recover the broken generators and show that, at the planar level, a version of the full SU(4) symmetry is still present. I will briefly discuss the implications of this hidden symmetry as far as the planar spectrum of the theory is concerned.

I will discuss the Hopf algebraic (quantum symmetry) structures underlying certain four-dimensional finite quantum field theories which are related to the N=4 SYM theory by marginal deformations. The motivation is to understand why these theories, despite being finite (like N=4 SYM), are generically not integrable in the planar limit (unlike N=4 SYM). Apart from a better understanding of integrability, these hidden symmetries might eventually provide insight into the construction of the (still unknown) dual AdS/CFT geometries for these field theories.