Diagrams for Symmetric Product Orbifolds

Abstract

We develop a diagrammatic language for symmetric product orbifolds of two-dimensional conformal field theories. Correlation functions of twist operators are written as sums of diagrams: each diagram corresponds to a branched covering map from a surface where the fields are single-valued to the base sphere where twist operators are inserted. This diagrammatic language facilitates the study of the large N limit and makes more transparent the analogy between symmetric product orbifolds and free non-abelian gauge theories. We give a general algorithm to calculate the leading large N contribution to four-point correlators of twist fields.

43 pages, 19 figures, v2: references added

References in corpus (4)

• Matching of correlators in AdS_3/CFT_2
• Exact N=4 correlators of AdS(3)/CFT(2)
• Simplifying and Extending the AdS_5xS^5 Pure Spinor Formalism
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Cited by in corpus (88)

• The Worldsheet Dual of the Symmetric Product CFT
• Emergent Spacetime and Holographic CFTs
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Bounding the Space of Holographic CFTs with Chaos
• Strings on NS-NS Backgrounds as Integrable Deformations
• Superstrings on AdS3 at k=1
• Kerr/CFT, dipole theories and nonrelativistic CFTs
• A Spin Chain for the Symmetric Product CFT_2
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Towards integrability for AdS3/CFT2
• Deforming the D1D5 CFT away from the orbifold point
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• Partition functions of the tensionless string
• S-matrix for magnons in the D1-D5 system
• Excitations in the deformed D1D5 CFT
• Phase transitions in symmetric orbifold CFTs and universality
• Correlators of the symmetric product orbifold
• Effect of the deformation operator in the D1D5 CFT
• Universality of Sparse $d>2$ Conformal Field Theory at Large $N$
• Emission from the D1D5 CFT: Higher Twists
• Operator mixing for string states in the D1-D5 CFT near the orbifold point
• Lifting of D1-D5-P states
• Effect of the twist operator in the D1D5 CFT
• Localization and AdS/CFT Correspondence
• Bogoliubov coefficients for the twist operator in the D1D5 CFT
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• Three-point functions in AdS${}_3$/CFT${}_2$ holography
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• Twist-nontwist correlators in M^N/S_N orbifold CFTs
• Genus Two Partition Functions and Renyi Entropies of Large c CFTs
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• Comments on the $S_N$ orbifold CFT in the large $N$-limit
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• Analyzing the squeezed state generated by a twist deformation
• Lifting at higher levels in the D1D5 CFT
• The Spectrum of Boundary States in Symmetric Orbifolds
• Full action of two deformation operators in the D1D5 CFT
• Beyond the Tensionless Limit: Integrability in the Symmetric Orbifold
• $\mathcal{N}=2$ Minimal Models: A Holographic Needle in a Symmetric Orbifold Haystack
• Lifting of level-1 states in the D1D5 CFT
• Large-N limits of 2d CFTs, Quivers and AdS_3 duals
• The OPE of bare twist operators in bosonic $S_N$ orbifold CFTs at large $N$
• Microstate Renormalization in Deformed D1-D5 SCFT
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Universal lifting in the D1-D5 CFT
• Perturbing the symmetric orbifold from the worldsheet
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Permutation Orbifolds and Chaos
• Entanglement versus entwinement in symmetric product orbifolds
• Warped AdS_3 Black Holes in Higher Derivative Gravity Theories
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• The Stranger Things of Symmetric Product Orbifold CFTs
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Lifting of states in 2-dimensional $N=4$ supersymmetric CFTs
• Lifting 1/4-BPS States on K3 and Mathieu Moonshine
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• One-Loop Transition Amplitudes in the D1D5 CFT
• The Holographic Landscape of Symmetric Product Orbifolds
• Intertwining Relations for the Deformed D1D5 CFT
• Stress-energy tensor correlators from the world-sheet
• D1 and D5-brane giant gravitons on $Ad{S}_3\times S^3\times S^3\times S^1$
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• Twistor Coverings and Feynman Diagrams
• The large $N$ limit of OPEs in symmetric orbifold CFTs with $\mathcal{N}=(4,4)$ supersymmetry
• Dynamics of R-neutral Ramond fields in the D1-D5 SCFT
• Thermalization in the D1D5 CFT
• Bosonization, cocycles, and the D1-D5 CFT on the covering surface
• The Topological Symmetric Orbifold
• Fractional Conformal Descendants and Correlators in General 2D $S_N$ Orbifold CFTs at Large $N$
• A localising AdS${}_3$ sigma model
• Dynamical evolution in the D1D5 CFT
• Bootstrapping the effect of the twist operator in symmetric orbifold CFTs
• From Matrices to Strings and Back
• Symmetric Product Orbifold Universality and the Mirage of an Emergent Spacetime
• The Dual of a Tidal Force in the D1D5 CFT
• Free Fermion Cyclic/Symmetric Orbifold CFTs and Entanglement Entropy
• Larger Twists and Higher $n$-Point Functions with Fractional Conformal Descendants in $S_N$ Orbifold CFTs at Large $N$
• Perturbed symmetric-product orbifold: first-order mixing and puzzles for integrability
• Conformal field theories dual to quantum gravity with strongly coupled matter
• Second order effect of twist deformation in the D1D5 CFT
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Symmetric Group Gauge Theories and Simple Gauge/String Dualities
• Hexagonalization in $Ad{S}_3\times S^3\times T^4$: Mirror Corrections
• Space-time symmetry from the world-sheet
• A New Supersymmetry Index for the D1-D5 CFT
• Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence
• Searching for strongly coupled AdS matter with multi-trace deformations
• Lecture notes on strings in AdS${}_3$ from the worldsheet and the AdS${}_3$/CFT${}_2$ duality