AdS and pp-wave D-particle superalgebras

TL;DR

This paper derives the superalgebra structures involving D-particles in AdS(2) x S(2) and pp-wave backgrounds, revealing how brane charges depend on position and can be incorporated into bosonic generators.

Contribution

It introduces a method to derive superalgebras with brane charges in specific backgrounds using coset constructions and supermatrix coordinates.

Findings

Brane charges depend on position in the superalgebras.

Brane charges can be absorbed into bosonic generators via momentum shifts.

Closure of superalgebras is achieved through this absorption process.

Abstract

We derive anticommutators of supercharges with a brane charge for a D-particle in AdS(2) x S(2) and pp-wave backgrounds. A coset GL(2|2)/(GL(1))^4 and its Penrose limit are used with the supermatrix-valued coordinates for the AdS and the pp-wave spaces respectively. The brane charges have position dependence, and can be absorbed into bosonic generators by shift of momenta which results in closure of the superalgebras.