Lectures on Branes in Curved Backgrounds

Abstract

These lectures provide an introduction to the microscopic description of branes in curved backgrounds. After a brief reminder of the flat space theory, the basic principles and techniques of (rational) boundary conformal field theory are presented in the second lecture. The general formalism is then illustrated through a detailed discussion of branes on compact group manifolds. In the final lecture, many more recent developments are reviewed, including some results for non-compact target spaces.

109 pages, 11 figures, Lectures presented at the third RTN school on `The Quantum Structure of Spacetime and the Geometric Nature of Fundamental Interactions', Utrecht, January 2002

Cited by in corpus (56)

• Symmetry, Gravity and Noncommutativity
• Holography, Entanglement Entropy, and Conformal Field Theories with Boundaries or Defects
• Fusion of conformal interfaces
• Conformal boundary loop models
• D-branes and extended characters in SL(2,R)/U(1)
• Abelian and non-Abelian branes in WZW models and gerbes
• Branes in the GL(1|1) WZNW-Model
• Stochastic Loewner evolution for conformal field theories with Lie-group symmetries
• D-branes in N=2 WZW models
• The deformation quantizations of the hyperbolic plane
• Boundary Liouville theory at c=1
• Exact Solutions in SFT and Marginal Deformation in BCFT
• Cosmology with Branes Wrapping Curved Internal Manifolds
• Boundary Correlators in Supergroup WZNW Models
• The General Twisted Open WZW String
• Noncommutative Field Theory on Homogeneous Gravitational Waves
• Symmetry breaking, permutation D-branes on group manifolds: boundary states and geometric description
• Canonical approach to the closed string noncommutativity
• Discrete D-branes in AdS3 and in the 2d black hole
• Normal ordering and noncommutativity in open bosonic strings
• Boundary action of the H3+ model
• Geometry of open strings ending on backreacting D3-branes
• Non-abelian Toda theory on AdS${}_2$ and AdS${}_2$/CFT${}_2^{1/2}$ duality
• Normal ordering and boundary conditions in open bosonic strings
• Super D-branes from BRST Symmetry
• D-branes in $\lambda$-deformations
• Liouville D-branes in Two-Dimensional Strings and Open String Field Theory
• Topological Cigar and the c=1 String : Open and Closed
• Noncommutativity in weakly curved background by canonical methods
• Superconformal boundary conditions for the WZW model
• Star products on extended massive non-rotating BTZ black holes
• Nongeometric background arising in the solution of Neumann boundary conditions
• Non-commutativity parameters depend not only on the effective coordinate but on its T-dual as well
• The WZW model on Random Regge Triangulations
• Algebraic brane dynamics on SU(2): excitation spectra
• Level-rank duality of D-branes on the SU(N) group manifold
• Level-rank duality of untwisted and twisted D-branes
• Isometric Embeddings and Noncommutative Branes in Homogeneous Gravitational Waves
• Special holonomy sigma models with boundaries
• On modular properties of the AdS3 CFT
• Rolling tachyon in anti-de Sitter space-time
• Kondo flow invariants, twisted K-theory and Ramond-Ramond charges
• $\lambda$-deformations in the upper-half plane
• Open string T-duality in a weakly curved background
• A mathematical formalism for the Kondo effect in WZW branes
• Brane Bulk Couplings and Condensation from REA Fusion
• Quantum Matrix Models for Simple Current Orbifolds
• Twisted D-branes of the SU(N)_K WZW model and level-rank duality
• YM on the dielectric brane: a D0-brane tale
• D-branes with Lorentzian signature in the Nappi-Witten model
• Twisted WZW Branes from Twisted REA's
• The scientific work of Sonia Stanciu
• On Factorization Constraints for Branes in the H3+ Model
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Perturbative deformations of conformal field theories revisited
• A Defect in AdS3/CFT2 Duality