Penrose limits of I-branes, twist-compactified D5-branes, and spin chains

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 (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:mn>1</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:mrow></a:math>) dimensions]. The second consists of D5-branes compactified on a circle. Both compactifications preserve supersymmetry. We find a match of the oscillators and masses of string modes on the resulting pp wave against a spin chain in a (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mrow><c:mn>2</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:mrow></c:math>)-dimensional field theory in the first case, and a spin chain in a (<e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mrow><e:mn>1</e:mn><e:mo>+</e:mo><e:mn>1</e:mn></e:mrow></e:math>)-dimensional field theory in the second.