Superconformal Actions in Killing Gauge

TL;DR

This paper demonstrates that superconformal actions of branes in AdS superspaces simplify significantly when gauge-fixed using Killing spinors, due to the vanishing of a key matrix, revealing a deep algebraic relation.

Contribution

It shows that gauge-fixing with Killing spinors leads to a dramatic simplification of superconformal brane actions by setting M^2=0, clarifying the algebraic structure involved.

Findings

Superconformal actions simplify when gauge-fixed with Killing spinors.

The matrix M^2 becomes zero in these gauges, simplifying the action.

The relation between classical and gauge-fixed actions reflects algebraic structures.

Abstract

The classical superconformal actions of branes in adS superspaces have a closed form depending on a matrix $M^2$ quadratic in fermions, as found in hep-th/9805217. One can gauge-fix the local $\kappa$-symmetry using the Killing spinors of the brane in the bulk. We show that in such gauges the superconformal actions are simplified dramatically since $M^2=0$ in all cases. The relation between classical and gauge-fixed actions for these theories reflects the relation between the full superconformal algebra and its supersolvable subalgebra.