(see [@BHTZ] section 3.2.4). Nevertheless this shows that (\[BTZ\]) with non-periodic coordinate $x'$ describes anti-de Sitter spacetime. Therefore, so does (\[adS3W\]). Note also that the wave does not contribute to the antisymmetric field strength. Thus the near-horizon limit of $M2\perp M5 + W$ is the same as that of $M2\perp M5$. We conclude then also that the supersymmetry of $M2\perp M5+W$ ($1/8$) is enhanced to $1/2$. If we dimensionally reduce the metric (\[adS3W\]) on $x$, we get $adS_2$ (times $E^5 \xx S^3$) with a covariantly constant two-form Kaluza-Klein field strength, and zero dilaton. This type IIA solution is the near-horizon limit of a $D0\perp F1\perp D4$ intersection. It preserves $1/4$ of supersymmetry since only half of the $adS_3$ Killing spinors survive the reduction. This can be seen from the explicit form of the Killing spinors as given in [@CH]. The surviving $adS_2$ Killing spinors in the resulting coordinate frame are the ones given in [@LPT].

The $D0\perp F1\perp D4$ configuration can be lifted to a $D=11$ solution built only out of two and five-branes after first $T$-dualizing along two relative transverse directions parallel to the $D4$ brane. This yields $M2\perp M2\perp M2$ with near-horizon geometry $adS_2 \xx E^6 \xx S^3$. 