On the perturbative chiral ring for marginally deformed N=4 SYM theories

Details On the perturbative chiral ring for marginally deformed N=4 SYM theories On the perturbative chiral ring for marginally deformed N=4 SYM theories

2006-05-15

arxiv.org/abs/hep-th/0605145v2

JHEP0608:072,2006

Physics

High Energy Physics

High Energy Physics - Theory

LaTex, 40 pages, 4 figures, uses JHEP3; v2: minor corrections

Scientific paper

10.1088/1126-6708/2006/08/072

For \cal{N}=1 SU(N) SYM theories obtained as marginal deformations of the \cal{N}=4 parent theory we study perturbatively some sectors of the chiral ring in the weak coupling regime and for finite N. By exploiting the relation between the definition of chiral ring and the effective superpotential we develop a procedure which allows us to easily determine protected chiral operators up to n loops once the superpotential has been computed up to (n-1) order. In particular, for the Lunin-Maldacena beta-deformed theory we determine the quantum structure of a large class of operators up to three loops. We extend our procedure to more general Leigh-Strassler deformations whose chiral ring is not fully understood yet and determine the weight-two and weight-three sectors up to two loops. We use our results to infer general properties of the chiral ring.

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