Supersymmetry of consistent massive truncations of IIB supergravity

TL;DR

This paper analyzes the supersymmetry and fermionic sectors of consistent massive truncations of IIB supergravity, providing explicit transformations, equations, and applications to known solutions and flux compactifications.

Contribution

It presents the general form of supersymmetry transformations and equations for fermions in five-dimensional N=4 truncations of IIB supergravity, including explicit Killing spinors and superpotentials.

Findings

Derived N=4 supersymmetry transformations for IIB truncations.

Constructed explicit Killing spinors for the Klebanov-Strassler solution.

Applied truncation methods to flux compactifications with SU(2) structure.

Abstract

We discuss the supersymmetry and fermionic sector of the recently obtained consistent truncations of IIB supergravity containing massive modes. In particular, we present the general form of the five-dimensional N = 4 supersymmetry transformations and equations of motion for the fermions arising in the reduction of IIB theory on T^{1,1} which contains all modes invariant under the SU(2) x SU(2) isometry group. The N = 4 reduction can be further truncated to two different N = 2 sub-sectors. For each of these, we present the N = 2 fermionic supersymmetry transformations and corresponding superpotentials. As an application, we obtain the explicit Killing spinors of the Klebanov-Strassler solution and comment on the relation to the ansatz of Papadopoulos and Tseytlin. We also demonstrate the applicability of consistent truncations on squashed Sasaki-Einstein manifolds to a class of flux compactifications, focusing on a recent solution describing the geometry of gaugino condensation on wrapped D7 branes and which possesses dynamic SU(2) structure.