Supersymmetry of rotating branes

Abstract

We present a new $1/8$ supersymmetric intersecting M-brane solution of $D=11\mathrm{}$ supergravity with two independent rotation parameters. The metric has a non-singular event horizon and the near-horizon geometry is ${\mathrm{AdS}}_3{\times \mathrm{S}}^3{\times \mathrm{S}}^3\times E^2$ (just as in the non-rotating case). We also present a method of determining the isometry supergroup of supergravity solutions from the Killing spinors and use it to show that for the near horizon solution it is $D(2\mathrm{}|1,\alpha )\times D(2\mathrm{}|1,\alpha )$ where α is the ratio of the two 3-sphere radii. We also consider various dimensional reductions of our solution, and the corresponding effect of these reductions on the Killing spinors and the isometry supergroups.