Double Field Theory, T-Duality, and Courant Brackets

Abstract

These lecture notes are based on three lectures, each ninety minutes long, given by the author at the "International School on Strings and Fundamental Physics" which took place in Garching/Munich from July 25 to August 6, 2010. These lectures, aimed at graduate students, require only a basic knowledge of string theory and give a simple introduction to double field theory. These notes were prepared by Marco Baumgartl and Nicolas Moeller.

25 pages

References in corpus (2)

• Double Field Theory
• The gauge algebra of double field theory and Courant brackets

Cited by in corpus (49)

• Double Field Theory: A Pedagogical Review
• The Spacetime of Double Field Theory: Review, Remarks, and Outlook
• Double Field Theory and N=4 Gauged Supergravity
• Exploring Double Field Theory
• Duality orbits of non-geometric fluxes
• Exotic Branes in String Theory
• Large Gauge Transformations in Double Field Theory
• Born Reciprocity in String Theory and the Nature of Spacetime
• Quantum Gravity, Dynamical Phase Space and String Theory
• Gauge theory of Kaluza-Klein and winding modes
• Non-associative Deformations of Geometry in Double Field Theory
• Generalized gravity from modified DFT
• Quantum Spaces are Modular
• Generalised fluxes, Yang-Baxter deformations and the O(d,d) structure of non-abelian T-duality
• Towards an invariant geometry of double field theory
• Even symplectic supermanifolds and double field theory
• U-duality covariant gravity
• SL(5) duality from canonical M2-brane
• Generalized Dualities and Higher Derivatives
• Canonical approach to Courant brackets for D-branes
• Extended Riemannian Geometry I: Local Double Field Theory
• M5 algebra and SO(5,5) duality
• Double Field Theory Inspired Cosmology
• Yang-Baxter Deformation as an O(d,d) Transformation
• Canonical formulation and conserved charges of double field theory
• Non-Abelian T-duality as a Transformation in Double Field Theory
• On current algebras, generalised fluxes and non-geometry
• A note on large gauge transformations in double field theory
• Gravity theory on Poisson manifold with $R$-flux
• Star products on graded manifolds and ${\alpha }^{\prime }$-corrections to Courant algebroids from string theory
• Semi-doubled Sigma Models for Five-branes
• T-duality Transformation of Gauged Linear Sigma Model with F-term
• Duality Twisted Reductions of Double Field Theory of Type II Strings
• Currents, charges and algebras in exceptional generalised geometry
• Metastring Theory and Modular Space-time
• New Cosmological Signatures from Double Field Theory
• Asymptotic symmetry groups and operator algebras
• Metric algebroid and Dirac generating operator in Double Field Theory
• The Algebra of Diffeomorphisms from the World Sheet
• O(D,D) gauge fields in the T-dual string Lagrangian
• Perturbative F-theory 10-brane and M-theory 5-brane
• String Excitation by Initial Singularity of Inflation
• Lie algebroids, non-associative structures and non-geometric fluxes
• Metric Algebroid and Poisson-Lie T-duality in DFT
• Loop Corrections in Double Field Theory: Non-trivial Dilaton Potentials
• Gauged Supergravities and the Physics of Extra Dimensions
• Pin(d,d) covariance of pure spinor equations for supersymmetric vacua and Non-Abelian T-duality
• $O(d,d;\mathbb{Z})$ invariant Fierz-Pauli massive gravity
• Black hole solutions in double field theory