Abstract
We classify supersymmetric warped AdS3×wM7 backgrounds of Type IIA and Type IIB supergravity with non-constant dilaton, generic RR fluxes and magnetic NSNS flux, in terms of a dynamic SU(3)-structure on M7. We illustrate our results by recovering several solutions with various amounts of supersymmetry. The dynamic SU(3)-structure includes a G2-structure as a limiting case, and we show that in Type IIB this is integrable.
Highlights
JHEP08(2021)168 reduce the problem of finding a solution to the supersymmetry equations and the equations of motion, to a single geometric equation
We briefly summarize the mathematical formalism for G2- and SU(3)-structures on sevendimensional Riemannian manifolds that we will use in analyzing the supersymmetry equations (2.12)
The RR and NSNS field-strengths are expressed in terms of the SU(3)-structure data
Summary
We consider bosonic backgrounds of Type II supergravity whose spacetime is a warped product AdS3 ×w M7, where M7 is a seven-dimensional Riemannian manifold. An SU(3)-structure on a seven-dimensional Riemannian manifold M7 is defined by a nowhere-vanishing, globally defined triplet comprising a real one-form v, a real two-form J, and a complex decomposable three-form Ω, subject to the following defining relations: i v J = v Ω = 0, Ω∧J = 0, Ω∧Ω = J ∧J ∧J. The intrinsic torsion of an SU(3)-structure splits into torsion classes, which transform in irreducible representations of SU(3) They parameterize the exterior derivatives of (v, J, Ω) as: dv = RJ + T1 + Re(V1 Ω) + v ∧ W0 , dJ = 2 Im(W1Ω) + W3 + W4 ∧ J + v ∧. We may decompose the three-form φ defined by the spinor χ1 = χ2 in terms of an SU(3)-structure (v, J, Ω), leading to the above result even in this limiting case. The phase eiθ multiplying Ω can be “absorbed” by a redefinition eiθΩ → Ω, and we will apply this redefinition
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