Penrose limit and NCYM theories in diverse dimensions

Abstract

We obtain the Penrose limit of NCYM theories in dimensions $3\le d\le 6$ which originate from (D$(p-2)$, D$p$) supergravity bound state configurations for $2\le p\le 5$ in the so-called NCYM limit. In most cases the Penrose limit does not lead to solvable string theories except for six-dimensional NCYM theory. We obtain the masses of various bosonic coordinates and observe that they are light-cone time dependent and their squares can be negative as has also been observed in other cases in the literature. When the non-commutative effect is turned off we recover the results of Penrose limit of ordinary D$p$-branes in the usual YM limit. We point out that for $d=6$ NCYM theory, there exists another null geodesic in the neighborhood of which the Penrose limit leads to a solvable string theory. We briefly discuss the quantization of this theory and show that this pp-wave background is half supersymmetric.

latex, 22 pages, physical meaning of the choice of the parameter $l=1$ is given, comments on the negative mass^2 added and the background is shown to be half supersymmetric, references added, published version

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• On the Singularity Structure and Stability of Plane Waves
• Penrose Limit and String Theories on Various Brane Backgrounds
• String theory and the Classical Stability of Plane Waves
• Penrose Limit and Six-Dimensional Gauge Theories
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