BMN Operators for Script N = 1 superconformal Yang-Mills theories and associated string backgrounds

We study a class of near-BPS operators for a complex 2-parameter family of = 1 superconformal Yang-Mills theories that can be obtained by a Leigh-Strassler deformation of = 4 SYM theory. We identify these operators in the large-N and large R-charge limit and compute their exact scaling dimensions using = 1 superspace methods. From these scaling dimensions we attempt to reverse-engineer the light-cone worldsheet theory that describes string propagation on the Penrose limit of the dual geometry.

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