Nonrenormalization theorems

[blefloch]

• In 4d N=1, superpotential can only receive instanton corrections (hence only if there are vector multiplets).
• In 4d N=2, Higgs branch has a hyperKahler metric, not renormalized, independent of Coulomb branch moduli; Coulomb branch is rigid special Kahler manifold independent of Higgs branch moduli. See http://arxiv.org/abs/hep-th/9603042 . The beta function is one-loop exact.
• 4d N=4 SYM is exactly conformal: see http://inspirehep.net/record/23243
• In 3d N=2, the superpotential depends on chirals but not on FI and real mass, the central charge depends on FI and real mass but not on chirals. See "Aspects of ..." paper.
• In 3d N=3, R-symmetry is nonabelian, so in CFTs dimensions are not renormalized.
• In 3d N=4, well-defined notion of Coulomb/Higgs branch, Higgs branch metric not renormalized.
• In 2d N=(2,2), only divergence is logarithmic divergence of FI

[blefloch]

http://arxiv.org/abs/hep-th/9401053 http://arxiv.org/abs/0704.3740

[blefloch]

Maybe also say "super-renormalizable = only a finite number of divergent diagrams survive", finite etc.

Redundant operators of a CFT are operators that vanish in any correlation function at separated points.