Spacetime superalgebra inAdS4×S7via the supermembrane probe

Abstract

The spacetime superalgebra via the supermembrane probe in the background of ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{7}$ is discussed to the lowest order in the spinor coordinate $\ensuremath{\theta}$. To obtain the correct spacetime superalgebras, all ${\ensuremath{\theta}}^{2}$ order corrections for a supervielbein and super 3-form gauge potential have to be included. The central extension of the superalgebra $OSp(8|4)$ of the superisometries for ${\mathrm{AdS}}_{4}\ifmmode\times\else\texttimes\fi{}{\mathrm{S}}^{7}$ is found.