In this paper we consider the Penrose limit in the case of two gravity duals. One of them, consists of compactified I-branes (intersecting sets of D5-branes over $(1+1)$ dimensions). The second consists of D5-branes compactified on a circle. Both compactifications preserve SUSY. We find a match of the oscillators and masses of string modes on the resulting pp wave against a spin chain in a $(2+1)-$dimensional field theory in the first case, and a spin chain in a $(1+1)-$dimensional field theory in the second.
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Barbosa et al. (2024) studied this question.
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