Non-compact String Backgrounds and Non-rational CFT

Abstract

This is an introduction to the microscopic techniques of non-rational bulk and boundary conformal field theory which are needed to describe strings moving in non-compact curved backgrounds. The latter arise e.g. in the context of AdS/CFT-like dualities and for studies of time-dependent processes. After a general outline of the central concepts, we focus on two specific but rather prototypical models: Liouville field theory and the 2D cigar. Rather than following the historical path, the presentation attempts to be systematic and self-contained.

85 pages, 8 figures, lecture notes

References in corpus (16)

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• The Annular Report on Non-Critical String Theory
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• Boundary Liouville theory at c=1
• D-branes and BCFT in Hpp-wave backgrounds
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• Paperclip at $\theta =\pi$
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• Modular Bootstrap of Boundary N=2 Liouville Theory

Cited by in corpus (38)

• Logarithmic Conformal Field Theory: Beyond an Introduction
• H^+_3 WZNW model from Liouville field theory
• Conformal boundary loop models
• An integrable spin chain for the SL(2,R)/U(1) black hole sigma model
• Conformal field theory on the plane
• The FZZ-Duality Conjecture - A Proof
• Notes on Liouville Theory at c<=1
• Coulomb integrals for the SL(2,R) WZNW model
• Scaling limit of the ${\mathcal{Z}}_2$ invariant inhomogeneous six-vertex model
• On Superstring Disk Amplitudes in a Rolling Tachyon Background
• Degenerate operators in JT and Liouville (super)gravity
• Exact surface energy and helical spinons in the XXZ spin chain with arbitrary non-diagonal boundary fields
• A lattice approach to the conformal $\OSp(2S+2|2S)$ supercoset sigma model. Part II: The boundary spectrum
• Discrete D-branes in AdS3 and in the 2d black hole
• Lattice regularisation of a non-compact boundary conformal field theory
• Boundary action of the H3+ model
• Liouville theory without an action
• Twisted boundary states and representation of generalized fusion algebra
• Critical Boundary Sine-Gordon Revisited
• The Floquet Baxterisation
• FZZ Algebra
• Liouville's Imaginary Shadow
• Some remarks on D-branes and defects in Liouville and Toda field theories
• Equilibrium density matrices for the 2D black hole sigma models from an integrable spin chain
• Limit theories and continuous orbifolds
• Three- and four-point connectivities of two-dimensional critical $Q-$ Potts random clusters on the torus
• On the CFT describing the spin clusters in 2d Potts model
• Disk one-point function for non-rational conformal theories
• Canonical approach to the WZNW model
• Scaling limit of the staggered six-vertex model with $U_q(\mathfrak{sl}(2))$ invariant boundary conditions
• The chiral SYK model in three-dimensional holography
• The $D_3^{(2)}$ spin chain and its finite-size spectrum
• D-branes with Lorentzian signature in the Nappi-Witten model
• On the Various Types of D-Branes in the Boundary H3+ Model
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality
• Quantum-group-invariant $D_{n+1}^{(2)}$ models: Bethe ansatz and finite-size spectrum
• Continuously Crossing u=z in the H3+ Boundary CFT
• On Factorization Constraints for Branes in the H3+ Model