Pure spinor equations to lift gauged supergravity

TL;DR

This paper presents a new method to lift gauged supergravity solutions to ten dimensions using pure spinor equations, avoiding complex truncations and unphysical multiplets.

Contribution

It introduces a formal rewriting of ten-dimensional supersymmetry equations as a G-structure system in N=2 gauged supergravity using pure spinors and fluxes.

Findings

Provides a framework to find lifts of BPS solutions.

Eliminates the need for consistent truncation.

Avoids unphysical gravitino multiplets.

Abstract

We rewrite the equations for ten-dimensional supersymmetry in a way formally identical to a necessary and sufficient G-structure system in N=2 gauged supergravity, where all four-dimensional quantities are replaced by combinations of pure spinors and fluxes in the internal space. This provides a way to look for lifts of BPS solutions without having to reduce or even rewrite the ten-dimensional action. In particular this avoids the problem of consistent truncation, and the introduction of unphysical gravitino multiplets.