Generalized geometry, calibrations and supersymmetry in diverse dimensions

Abstract

We consider type II backgrounds of the form R^{1,d-1} x M^{10-d} for even d, preserving 2^{d/2} real supercharges; for d = 4, 6, 8 this is minimal supersymmetry in d dimensions, while for d = 2 it is N = (2,0) supersymmetry in two dimensions. For d = 6 we prove, by explicitly solving the Killing-spinor equations, that there is a one-to-one correspondence between background supersymmetry equations in pure-spinor form and D-brane generalized calibrations; this correspondence had been known to hold in the d = 4 case. Assuming the correspondence to hold for all d, we list the calibration forms for all admissible D-branes, as well as the background supersymmetry equations in pure-spinor form. We find a number of general features, including the following: The pattern of codimensions at which each calibration form appears exhibits a (mod 4) periodicity. In all cases one of the pure-spinor equations implies that the internal manifold is generalized Calabi-Yau. Our results are manifestly invariant under generalized mirror symmetry.

arXiv comment28 pages, 1 table

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Cited by in corpus (24)

• All AdS_7 solutions of type II supergravity
• Supersymmetry on Curved Spaces and Holography
• AdS_6 solutions of type II supergravity
• AdS${}_3$ solutions in Massive IIA with small $\mathcal{N}=(4,0)$ supersymmetry
• Rigid supersymmetric theories in 4d Riemannian space
• Type II Solutions on AdS${}_3\times S^3\times S^3$ with Large Superconformal Symmetry
• Generalized structures of ten-dimensional supersymmetric solutions
• Supersymmetric Backgrounds and Generalised Special Holonomy
• D-branes in Generalized Geometry and Dirac-Born-Infeld Action
• Minkowski${}_4$ $\times$ $S^2$ solutions of IIB supergravity
• Electrified branes
• IIA supergravity and M-theory on manifolds with SU(4) structure
• IIB supergravity on manifolds with SU(4) structure and generalized geometry
• A note on smeared branes in flux vacua and gauged supergravity
• Generalized geometry of two-dimensional vacua
• Breaking supersymmetry with pure spinors
• Geometric Constructions of Two Dimensional (0,2) SUSY Theories
• Generalized geometric vacua with eight supercharges
• Mink${}_3\times S^3$ solutions of type II supergravity
• Timelike structures of ten-dimensional supersymmetry
• Mink${}_4\times S^2$ Solutions of 10 and 11 Dimensional Supergravity
• Supersymmetric branes and instantons on curved spaces
• Generalized complex geometry of pure backgrounds in ten and eleven dimensions
• Mirror symmetry & supersymmetry on SU(4)-structure backgrounds