Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality

Abstract

These lecture notes, based on the course given at IPhT in November/December 2023, provide a pedagogical introduction to the study of strings in AdS${}_3$ backgrounds supported by NSNS flux from the worldsheet perspective, including a number of updates incorporating recent results. We attempt to give a self-contained overview of the state-of-the-art understanding of this topic, describing key aspects of its 25-year-long rich history alongside some important recent developments, with an emphasis on the computation of worldsheet correlation functions involving spectrally flowed insertions.

v2: Typos corrected. Clarifications and references added. Version accepted in SciPost Physics Lecture Notes

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• A truly marginal deformation of SL(2,R) in a null direction
• Spectral Flow in AdS(3)/CFT(2)
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• String theory on three dimensional black holes
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• $T\bar{T}$ and LST
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• String correlators on ${\text{AdS}}_3$: Three-point functions
• String Theory of Supertubes
• Little Strings, Long Strings, and Fuzzballs
• String theory at the tip of the cigar
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• Long strings and chiral primaries in the hybrid formalism
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• The Holographic Landscape of Symmetric Product Orbifolds
• Worldsheet computation of heavy-light correlators
• Infinite $\mathrm{T}\bar{\mathrm{T}}$-like symmetries of compactified LST
• Stress-energy tensor correlators from the world-sheet
• A proof for string three-point functions in AdS${}_3$
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• Superstrings in Thermal Anti-de Sitter Space
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• A localising AdS${}_3$ sigma model
• Holographic Weyl anomaly in string theory
• On spectrally flowed local vertex operators in AdS${}_3$
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• Correlation Functions in the TsT/$T\bar{T}$ Correspondence
• Classical geometry from the tensionless string
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• The physical states of the Hybrid Formalism
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• Tensionless strings on $Ad{S}_3\times S^3\times S^3\times S^1$
• Unravelling AdS${}_3$/CFT${}_2$ near the boundary
• String theory in twistor space and minimal tension holography
• Spectral flow and localisation in ${\text{AdS}}_3$ string theory
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• Three-charge black holes from the worldsheet
• From black holes to solvable irrelevant deformations and back
• Tensionless strings on ${\mathrm{AdS}}_3$ orbifolds
• Exact approaches on the string worldsheet
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• NS5-brane backgrounds and coset CFT partition functions
• Spectral flow and the exact AdS${}_3/$CFT${}_2$ chiral ring
• Superstrings near the conformal boundary of $\mathrm{Ad}{\mathrm{S}}_3$
• Twisted Strings in Three-dimensional Black Holes
• A superspace approach to AdS${}_3$ string theory
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