Penrose limit and NCYM theories in diverse dimensions

TL;DR

This paper explores the Penrose limits of non-commutative Yang-Mills theories across dimensions 3 to 6, revealing solvable string backgrounds only in six dimensions and analyzing their supersymmetry properties.

Contribution

It provides the first detailed analysis of Penrose limits for NCYM theories in various dimensions, identifying conditions for solvability and supersymmetry in the resulting string theories.

Findings

Most Penrose limits do not produce solvable string theories.

In six-dimensional NCYM, a solvable string background exists near a specific null geodesic.

The six-dimensional case preserves half of the supersymmetry.

Abstract

We obtain the Penrose limit of NCYM theories in dimensions $3 \leq d \leq 6$ which originate from (D$(p-2)$, D$p$) supergravity bound state configurations for $2 \leq p \leq 5$ 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.