Spacetime Superalgebra in AdS_4 \times S^7 via Supermembrane Probe

TL;DR

This paper derives the spacetime superalgebra for AdS_4 imes S^7 using a supermembrane probe, including necessary quadratic corrections, and identifies the central extension of the superisometry algebra OSp(8|4).

Contribution

It provides the first detailed derivation of the superalgebra with quadratic corrections in the supermembrane context for AdS_4 imes S^7.

Findings

Central extension of OSp(8|4) superalgebra identified.

Quadratic order corrections are essential for accurate superalgebra.

Supermembrane probe effectively captures superalgebra structure.

Abstract

The spacetime superalgebra via the supermembrane probe in the background of AdS_4 \times S^7 is discussed to the lowest order in the spinor coordinate $\t$. To obtain the correct spacetime superalgebras, all $\t^2$ order corrections for supervielbein and super 3-form gauge potential have to be included. The central extension of the superalgebra OSp(8|4) of the super isometries for AdS_4 \times S^7 is found.