Gromov-Witten/Hilbert versus AdS3/CFT2 Correspondence

Abstract

We consider the boundary dual of AdS3xS3xK3 for NS5-flux Q5=1, which is described by a sigma model with target space given by the d-fold symmetric product of K3. Building on results in algebraic geometry, we address the problem of deforming it away from the orbifold point from the viewpoint of topological strings. We propose how the 't Hooft expansion can be geometrized in terms of Gromov-Witten invariants and, in favorable settings, how it can be summed up to all orders in closed form. We consider an explicit example in detail for which we discuss the genus expansion around the orbifold point, as well as the divergence in the strong coupling regime. We find that within the domain of convergence, scale separation does not occur. However, in order for the mathematical framework to be applicable in the first place, we need to consider "reduced" Gromov-Witten invariants that fit, as we argue, naturally to topologically twisted N=4 strings. There are some caveats and thus to what extent this toy model captures the physics of strings on AdS3xS3xK3 remains to be seen.

39 pages, 4 figures; v4: typos corrected and minimal clarifications added

References in corpus (92)

• The Swampland: Introduction and Review
• AdS3 Black Holes and a Stringy Exclusion Principle
• The D1/D5 System And Singular CFT
• Strings in AdS_3 and the SL(2,R) WZW Model. Part 1: The Spectrum
• Microscopic Formulation of Black Holes in String Theory
• Hurwitz numbers and intersections on moduli spaces of curves
• Lectures on the Swampland Program in String Compactifications
• AdS and the Swampland
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Stringy gravity, interacting tensionless strings and massless higher spins
• The Worldsheet Dual of the Symmetric Product CFT
• Correlation functions for M^N/S_N orbifolds
• N=4 Topological Strings
• Three-point functions for M^N/S^N orbifolds with N=4 supersymmetry
• Deriving the ${\text{AdS}}_3/{\text{CFT}}_2$ Correspondence
• Higher Spins & Strings
• U(1) Charges and Moduli in the D1-D5 System
• Tensionless String Spectra on ${\mathrm{AdS}}_3$
• BPS States, String Duality, and Nodal Curves on K3
• Extremal Correlators in the AdS/CFT Correspondence
• Diagrams for Symmetric Product Orbifolds
• Instanton Strings and HyperKaehler Geometry
• Gravity from CFT on $S^N(X)$ CFT: Symmetries and Interactions
• Superstrings on AdS3 at k=1
• A non-renormalization theorem for chiral primary 3-point functions
• String Theory on AdS_3
• Worldsheet correlators in AdS(3)/CFT(2)
• A perturbative CFT dual for pure NS-NS AdS${}_3$ strings
• Curves on K3 surfaces and modular forms
• Extremal Correlators and Hurwitz Numbers in Symmetric Product Orbifolds
• Deforming the D1D5 CFT away from the orbifold point
• F-Theory, Spinning Black Holes and Multi-string Branches
• Free field world-sheet correlators for ${\mathrm{AdS}}_3$
• String Theory as a Higher Spin Theory
• $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3$ Tree-Level Correlators: Hidden Six-Dimensional Conformal Symmetry
• Partition functions of the tensionless string
• Matching of correlators in AdS_3/CFT_2
• Excitations in the deformed D1D5 CFT
• Supergravity one-loop corrections on AdS_7 and AdS_3, higher spins and AdS/CFT
• Tackling the SDC in AdS with CFTs
• The chiral ring of AdS3/CFT2 and the attractor mechanism
• Correlators of the symmetric product orbifold
• Higher spins on AdS${}_3$ from the worldsheet
• Exact N=4 correlators of AdS(3)/CFT(2)
• Effect of the deformation operator in the D1D5 CFT
• Spectral Flow in AdS(3)/CFT(2)
• Operator mixing for string states in the D1-D5 CFT near the orbifold point
• Twisted Supergravity and Koszul Duality: A case study in AdS${}_3$
• String correlators on ${\text{AdS}}_3$: Three-point functions
• Effect of the twist operator in the D1D5 CFT
• Higher genus correlators for tensionless ${\mathrm{AdS}}_3$ strings
• On Higher-Spin Points and Infinite Distances in Conformal Manifolds
• From Symmetric Product CFTs to ${\mathrm{AdS}}_3$
• String correlators on ${\text{AdS}}_3$: Analytic structure and dual CFT
• Deforming Symmetric Product Orbifolds: A tale of moduli and higher spin currents
• On Hurwitz numbers and Hodge integrals
• Lifting at higher levels in the D1D5 CFT
• Lifting 1/4-BPS States in $Ad{S}_3\times S^3\times T^4$
• Operator mixing in deformed D1D5 CFT and the OPE on the cover
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Full action of two deformation operators in the D1D5 CFT
• Lifting of level-1 states in the D1D5 CFT
• On the BPS sector in AdS_3/CFT_2 Holography
• Microstate Renormalization in Deformed D1-D5 SCFT
• Conformal Perturbation Theory for Twisted Fields
• Universal lifting in the D1-D5 CFT
• Worldsheet four-point functions in AdS(3)/CFT(2)
• BPS Correlators for ${\text{AdS}}_3/{\text{CFT}}_2$
• Perturbing the symmetric orbifold from the worldsheet
• Correlation functions of symmetric orbifold from AdS${}_3$ string theory
• Higher spins in the symmetric orbifold of K3
• Gromov-Witten invariants of the Hilbert schemes of points of a K3 surface
• AdS scale separation and the distance conjecture
• Loop equations and a proof of Zvonkine's $qr$-ELSV formula
• Correlation functions of composite Ramond fields in deformed D1-D5 orbifold SCFT${}_2$
• On the Dynamics of Protected Ramond Ground States in the D1-D5 CFT
• Symmetries and Covering Maps for the Minimal Tension String on $\mathbf{Ad}{\mathbf{S}}_3\times {\mathbf{S}}^3\times {\mathbf{T}}^4$
• The free field realisation of the BVW string
• Long strings and chiral primaries in the hybrid formalism
• The plane-wave spectrum from the worldsheet
• Renormalization of Twisted Ramond Fields in D1-D5 SCFT${}_2$
• A proof for string three-point functions in AdS${}_3$
• Topological String on AdS_3 x N
• The Topological Symmetric Orbifold
• Twisted String Theory in Anti-de Sitter Space
• Multiple cover formulas for K3 geometries, wall-crossing, and Quot schemes
• Classical geometry from the tensionless string
• Worldsheet operator product expansions and p-point functions in AdS3/CFT2
• Notes on the proof of the KKV conjecture
• The Chiral Ring of a Symmetric Orbifold and its Large N Limit
• Quasimaps to moduli spaces of sheaves on a $K3$ surface
• Quasimaps to moduli spaces of sheaves