Equations of motion from Cederwall's pure spinor superspace actions

TL;DR

This paper verifies that Cederwall's pure spinor superspace actions for super-Born-Infeld and supergravity accurately describe their interactions by expanding solutions around linearized states.

Contribution

It demonstrates that Cederwall's non-minimal pure spinor actions correctly reproduce the equations of motion for super-Born-Infeld and supergravity.

Findings

Expanded solutions match known linearized equations

Actions reproduce expected interactions

Confirmed BRST-invariance in the expanded solutions

Abstract

Using non-minimal pure spinor superspace, Cederwall has constructed BRST-invariant actions for $D=10$ super-Born-Infeld and $D=11$ supergravity which are quartic in the superfields. But since the superfields have explicit dependence on the non-minimal pure spinor variables, it is non-trivial to show these actions correctly describe super-Born-Infeld and supergravity. In this paper, we expand solutions to the equations of motion from Cederwall's actions to leading order around the linearized solutions and show that they correctly describe the interactions of $D=10$ super-Born-Infeld and $D=11$ supergravity.