On supersymmetric solutions of type IIB supergravity with general fluxes

TL;DR

The paper addresses constructing ${\cal N}=1$ supersymmetric backgrounds in type IIB supergravity with general fluxes while preserving 4D Poincaré invariance. It introduces a general Type D spinor Ansatz that employs an SU(2) internal structure, enabling $(3,0)$ and $(0,3)$ flux components absent in SU(3)-based analyses and removing the strict ISD constraint in broader contexts. By projecting the dilatino and gravitino variations onto SU(2) tensors, it derives flux decompositions, warp-factor relations, and intrinsic torsion conditions, showing that the internal manifold need not be complex and that new consistent solutions exist, including a simple non-compact example with $(0,3)$ flux. These results broaden the landscape of SUSY flux vacua and have potential implications for gauge/gravity duality, holographic RG flows, and nonzero superpotential terms $W = \int G \wedge \Omega$ in the dual field theories.

Abstract

We propose a general spinor Ansatz to find supersymmetric configurations preserving 4-dimensional Poincare' invariance in the context of type IIB supergravity in the presence of general fluxes. We show how this removes the imaginary-selfduality (ISD) constraint on the 3-form flux and present a simple example with nonvanishing (0,3) flux. To characterize the geometrical properties of such configurations we will use the tool of SU(2) structures on the internal space, which are naturally linked to the form of the Ansatz we propose.