Type IIB Solutions with Interpolating Supersymmetries

TL;DR

This paper constructs type IIB supergravity solutions with four supersymmetries that interpolate between known compactification scenarios, revealing internal manifolds with SU(3) holonomy and flux-dependent structures.

Contribution

It introduces a new class of interpolating solutions with non-Calabi-Yau internal manifolds and flux-dependent fields, expanding the landscape of supergravity backgrounds.

Findings

Internal manifolds have SU(3) holonomy with torsion.

All fluxes and the dilaton depend on a single function satisfying a nonlinear differential equation.

Solutions include configurations corresponding to D3/D5-brane bound states.

Abstract

We study type IIB supergravity solutions with four supersymmetries that interpolate between two types widely considered in the literature: the dual of Becker and Becker's compactifications of M-theory to 3 dimensions and the dual of Strominger's torsion compactifications of heterotic theory to 4 dimensions. We find that for all intermediate solutions the internal manifold is not Calabi-Yau, but has SU(3) holonomy in a connection with a torsion given by the 3-form flux. All 3-form and 5-form fluxes, as well as the dilaton, depend on one function appearing in the supersymmetry spinor, which satisfies a nonlinear differential equation. We check that the fields corresponding to a flat bound state of D3/D5-branes lie in our class of solutions. The relations among supergravity fields that we derive should be useful in studying new gravity duals of gauge theories, as well as possibly compactifications.