Calibrated cycles and T-duality

Abstract

For Hitchin's generalised geometries we introduce and analyse the concept of a structured submanifold which encapsulates the classical notion of a calibrated submanifold. Under a suitable integrability condition on the ambient geometry, these generalised calibrated cycles minimise a functional occurring as D-brane energy in type II string theories, involving both so-called NS-NS- and R-R-fields. Further, we investigate the behaviour of calibrated cycles under T-duality and construct non-trivial examples.

43 pages. v4: formalism and T-duality part considerably expanded

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Cited by in corpus (14)

• T-duality, Generalized Geometry and Non-Geometric Backgrounds
• The effective theory of type IIA AdS4 compactifications on nilmanifolds and cosets
• Deformations of calibrated D-branes in flux generalized complex manifolds
• Refining the boundaries of the classical de Sitter landscape
• D-brane networks in flux vacua, generalized cycles and calibrations
• New supersymmetric vacua on solvmanifolds
• Generalised geometries, constrained critical points and Ramond-Ramond fields
• Seeing through the String Landscape - a String Hunter's Companion in Particle Physics and Cosmology
• Towards mirror symmetry à la SYZ for generalized Calabi-Yau manifolds
• A no-go theorem for monodromy inflation
• Supersymmetric D-branes on flux backgrounds
• Calibrations on spaces with GxG-structure
• Calabi-Yau manifolds with $B$-fields
• An Introduction to Potential Theory in Calibrated Geometry