More on correlators and contact terms in {\cal N}=4 SYM at order g^4

Details More on correlators and contact terms in {\cal N}=4 SYM at order g^4 More on correlators and contact terms in {\cal N}=4 SYM at order g^4

2000-05-24

arxiv.org/abs/hep-th/0005223v1

Nucl.Phys. B593 (2001) 651-670

Physics

High Energy Physics

High Energy Physics - Theory

21 pages, 4 figures

Scientific paper

10.1016/S0550-3213(00)00633-7

We compute two-point functions of chiral operators Tr(\Phi^k) for any k, in {\cal N}=4 supersymmetric SU(N) Yang-Mills theory. We find that up to the order g^4 the perturbative corrections to the correlators vanish for all N. The cancellation occurs in a highly non trivial way, due to a complicated interplay between planar and non planar diagrams. In complete generality we show that this same result is valid for any simple gauge group. Contact term contributions signal the presence of ultraviolet divergences. They are arbitrary at the tree level, but the absence of perturbative renormalization in the non singular part of the correlators allows to compute them unambiguously at higher orders. In the spirit of the AdS/CFT correspondence we comment on their relation to infrared singularities in the supergravity sector.

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