Geometry of all supersymmetric type I backgrounds

Abstract

We find the geometry of all supersymmetric type I backgrounds by solving the gravitino and dilatino Killing spinor equations, using the spinorial geometry technique, in all cases. The solutions of the gravitino Killing spinor equation are characterized by their isotropy group in Spin(9,1), while the solutions of the dilatino Killing spinor equation are characterized by their isotropy group in the subgroup Sigma(P) of Spin(9,1) which preserves the space of parallel spinors P. Given a solution of the gravitino Killing spinor equation with L parallel spinors, L = 1,2,3,4,5,6,8, the dilatino Killing spinor equation allows for solutions with N supersymmetries for any 0 < N =< L. Moreover for L = 16, we confirm that N = 8,10,12,14,16. We find that in most cases the Bianchi identities and the field equations of type I backgrounds imply a further reduction of the holonomy of the supercovariant connection. In addition, we show that in some cases if the holonomy group of the supercovariant connection is precisely the isotropy group of the parallel spinors, then all parallel spinors are Killing and so there are no backgrounds with N < L supersymmetries.

73 pages. v2: minor changes, references added

References in corpus (33)

• Non-Kaehler String Backgrounds and their Five Torsion Classes
• Superstrings with Intrinsic Torsion
• G-Structures and Wrapped NS5-Branes
• Supersymmetric String Solitons
• Geometric Model for Complex Non-Kaehler Manifolds with SU(3) Structure
• Twistor spaces for HKT manifolds
• Complex geometry of conifolds and 5-brane wrapped on 2-sphere
• Geometry of Hyper-Kähler Connections with Torsion
• The intrinsic torsion of SU(3) and G_2 structures
• Maximally supersymmetric solutions of ten- and eleven-dimensional supergravities
• Vanishing Theorems and String Backgrounds
• Anomaly Cancellation and Smooth Non-Kahler Solutions in Heterotic String Theory
• Killing spinor equations in dimension 7 and geometry of integrable G_2-manifolds
• The spinorial geometry of supersymmetric backgrounds
• Breaking the M-waves
• A no-go theorem for string warped compactifications
• The spinorial geometry of supersymmetric heterotic string backgrounds
• Pluecker-type relations for orthogonal planes
• Finiteness and anomalies in (4,0) supersymmetric sigma models
• Holonomy groups and W-symmetries
• N=31 is not IIB
• Twistor Spaces for QKT Manifolds
• N=31, D=11
• Planes, branes and automorphisms: II. Branes in motion
• Anomaly, Fluxes and (2,0) Heterotic-String Compactifications
• Supergravity vacua and lorentzian Lie groups
• On the absence of BPS preonic solutions in IIA and IIB supergravities
• Parallelisable Heterotic Backgrounds
• Dilatonic Parallelizable NS-NS Backgrounds
• Connection with torsion, parallel spinors and geometry of Spin(7) manifolds
• Geometry of type II common sector N=2 backgrounds
• Aspects of spinorial geometry
• The Existence of Supersymmetric String Theory with Torsion

Cited by in corpus (50)

• Heterotic supersymmetry, anomaly cancellation and equations of motion
• All timelike supersymmetric solutions of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• Characterization of all the supersymmetric solutions of gauged N=1,d=5 supergravity
• The Killing superalgebra of ten-dimensional supergravity backgrounds
• All null supersymmetric backgrounds of N=2, D=4 gauged supergravity coupled to abelian vector multiplets
• Geometry of four-dimensional Killing spinors
• On a family of ${\alpha }^{\prime }$-corrected solutions of the Heterotic Superstring effective action
• Supersymmetric heterotic string backgrounds
• Killing-Yano equations and G-structures
• Gauduchon-Tod structures, Sim holonomy and De Sitter supergravity
• HKT Geometry and de Sitter Supergravity
• Classification, geometry and applications of supersymmetric backgrounds
• Heterotic Black Horizons
• New half supersymmetric solutions of the heterotic string
• Heterotic horizons, Monge-Ampere equation and del Pezzo surfaces
• Supersymmetric solutions of gauged five-dimensional supergravity with general matter couplings
• Spinorial geometry and Killing spinor equations of 6-D supergravity
• All the timelike supersymmetric solutions of all ungauged d=4 supergravities
• Heterotic supersymmetric backgrounds with compact holonomy revisited
• The supersymmetric solutions and extensions of ungauged matter-coupled N=1,d=4 supergravity
• Non-Kaehler Heterotic String Solutions with non-zero fluxes and non-constant dilaton
• Index theory and dynamical symmetry enhancement near IIB horizons
• M-theory backgrounds with 30 Killing spinors are maximally supersymmetric
• Supersymmetric AdS_3 solutions in Heterotic Supergravity
• Geometry and supersymmetry of heterotic warped flux AdS backgrounds
• Classification of IIB backgrounds with 28 supersymmetries
• IIB backgrounds with five-form flux
• Compact supersymmetric solutions of the heterotic equations of motion in dimension 5
• IIB black hole horizons with five-form flux and KT geometry
• M-Theory with Framed Corners and Tertiary Index Invariants
• Supersymmetric geometries of IIA supergravity I
• On the supersymmetric solutions of the Heterotic Superstring effective action
• IIB black hole horizons with five-form flux and extended supersymmetry
• M-Horizons
• Some Algebraic Aspects of Half-BPS Bound States in M-Theory
• Twisted form hierarchies, Killing-Yano equations and supersymmetric backgrounds
• Anomaly Corrected Heterotic Horizons
• Covariantly constant forms on torsionful geometries from world-sheet and spacetime perspectives
• Supersymmetric geometries of IIA supergravity III
• Invariant Killing spinors in 11D and type II supergravities
• Spinorial geometry, off-shell Killing spinor identities and higher derivative 5D supergravities
• TCFHs, hidden symmetries and type II theories
• Solution of heterotic Killing spinor equations and special geometry
• Spinors of real type as polyforms and the generalized Killing equation
• The quaternionic Heisenberg group and Heterotic String Solutions with non-constant dilaton in dimensions 7 and 5
• The Classification of Highly Supersymmetric Supergravity Solutions
• Supersymmetry Enhancement of Heterotic Horizons
• Supersymmetric Yang-Mills theory on conformal supergravity backgrounds in ten dimensions
• Killing Spinors -- Beyond Supergravity
• Geometric Realizability of Covariant Derivative Kähler Tensors for almost Pseudo-Hermitian and almost Para-Hermitian Manifolds