Quantum geometry of refined topological strings

DOI10.1007/JHEP11(2012)019zbMath1397.83117arXiv1105.0630OpenAlexW3105421628MaRDI QIDQ1796105

Cumrun Vafa, Daniel Krefl, Mina Aganagic, Miranda C. N. Cheng, Robbert Dijkgraaf

Publication date: 16 October 2018

Published in: Journal of High Energy Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1105.0630

zbMATH Keywords

matrix modelstopological strings

Mathematics Subject Classification ID

String and superstring theories in gravitational theory (83E30) String and superstring theories; other extended objects (e.g., branes) in quantum field theory (81T30)

Related Items

Non-perturbative quantum geometry, M-theory interpretation of the real topological string, Quantum geometry from the toroidal block, \(\Omega\)-deformation and quantization, Non-perturbative effects and the refined topological string, Topological strings and quantum spectral problems, Non-perturbative quantum geometry. II, Seiberg-Witten theory as a Fermi gas, \(q\)-Virasoro modular double and 3d partition functions, Instanton effects and quantum spectral curves, Matrix models from operators and topological strings, Blowup equations for refined topological strings, Refined black hole ensembles and topological strings, Introduction to Khovanov homologies. I. Unreduced Jones superpolynomial, The toroidal block and the genus expansion, Genus one correction to Seiberg-Witten prepotential from \(\beta\)-deformed matrix model, Dijkgraaf-Vafa conjecture and \(\beta\)-deformed matrix models, Instanton corrections of 1/6 BPS Wilson loops in ABJM theory, Super-quantum curves from super-eigenvalue models, Exact results for ABJ Wilson loops and open-closed duality, Wilson loops in 3d \( \mathcal{N} =4\) SQCD from Fermi gas, Holomorphic anomaly in gauge theory on ALE space, A solvable deformation of quantum mechanics, Orientifolding of the ABJ Fermi gas, TBA-like integral equations from quantized mirror curves, Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings, Exact quantization conditions for the relativistic Toda lattice, Quantization condition from exact WKB for difference equations, ABJM on ellipsoid and topological strings, Non-perturbative quantum geometry. III, Black hole quasinormal modes and Seiberg-Witten theory, Resumming the string perturbation series, Exact results in \( \mathcal{N}=8 \) Chern-Simons-matter theories and quantum geometry, Large \(N\) non-perturbative effects in \( \mathcal{N}=4 \) superconformal Chern-Simons theories, Five-dimensional gauge theories and the local B-model, 3d expansions of 5d instanton partition functions, Quantum spectral problems and isomonodromic deformations, Operators from mirror curves and the quantum dilogarithm, Matrix models from operators and topological strings. II, From CFT to Ramond super-quantum curves, M5-branes, toric diagrams and gauge theory duality, General omega deformations from closed string backgrounds, Deformed planar topological open string amplitudes on Seiberg-Witten curve, Topological strings from quantum mechanics, Exact quantization conditions, toric Calabi-Yau and non-perturbative topological string, An elliptic Virasoro symmetry in 6d, On Painlevé/gauge theory correspondence, Quantum mirror curve of periodic chain geometry, Operators and higher genus mirror curves, Refined topological strings on local \(\mathbb P^2 \), The \(\Omega \) deformed \(B\)-model for rigid \(N=2\) theories, Quantum curve and the first Painlevé equation, Refined toric branes, surface operators and factorization of generalized Macdonald polynomials, High order perturbation theory for difference equations and Borel summability of quantum mirror curves, Exact relativistic Toda chain eigenfunctions from separation of variables and gauge theory, Non-perturbative approaches to the quantum Seiberg-Witten curve, On the spectrum of the local \(\mathbb{P}^2\) mirror curve, Non-perturbative quantum mechanics from non-perturbative strings, The Liouville side of the vortex, Topological string geometry, Argyres-Douglas theories, Painlevé II and quantum mechanics, Quantum curves as quantum distributions, Instantons in the Hofstadter butterfly: difference equation, resurgence and quantum mirror curves, Symmetry breaking in quantum curves and super Chern-Simons matrix models, TBA equations and resurgent quantum mechanics, Note on quantum periods and a TBA-like system, Brane transitions from exceptional groups, Twisted 6d \((2, 0)\) SCFTs on a circle, New results in \(\mathcal N=2\) theories from non-perturbative string, Quantum representation of affine Weyl groups and associated quantum curves, Spectral theory and mirror curves of higher genus, Quantum geometry of resurgent perturbative/nonperturbative relations, The refined BPS index from stable pair invariants, Quantum periods and spectra in dimer models and Calabi-Yau geometries, Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit, BPS relations from spectral problems and blowup equations, Torus knots and mirror symmetry, Reconstructing GKZ via topological recursion, Quantum periods and TBA-like equations for a class of Calabi-Yau geometries, Bootstrapping ADE M-strings, Resurgence analysis of 2d Yang-Mills theory on a torus, On statistical models on super trees, ABCD of beta ensembles and topological strings, Knot homology and refined Chern-Simons index, Special colored superpolynomials and their representation-dependence, Refined Chern-Simons theory and \((q, t)\)-deformed Yang-Mills theory: semi-classical expansion and planar limit, Refined stable pair invariants for E-, M- and \([p,q\)-strings], Hanany-Witten transition in quantum curves, E-string quantum curve, Wavefunctions, integrability, and open strings, Quantized mirror curves and resummed WKB, Resonances and PT symmetry in quantum curves, Quantum curves and \(q\)-deformed Painlevé equations, 4d \(\mathcal{N} = 2\) supergravity observables from Nekrasov-like partition functions, Exact WKB methods in SU(2) \(\mathrm{N_f} = 1\), Exact WKB and the quantum Seiberg-Witten curve for 4d \(N = 2\) pure SU(3) Yang-Mills. Abelianization, Duality cascades and affine Weyl groups, A-polynomial, B-model, and quantization, Loop equations and topological recursion for the arbitrary-\(\beta\) two-matrix model, Painlevé representation of Tracy-Widom\(_\beta\) distribution for \(\beta=6\), Duality cascades and parallelotopes, WKB method and quantum periods beyond genus one, Resummations and non-perturbative corrections, Exact solutions to quantum spectral curves by topological string theory, The spectral problem of the ABJ Fermi gas, Exact Chern-Simons / topological string duality, Spectral zeta function and non-perturbative effects in ABJM Fermi-gas, Developments in topological gravity, Spectral theories and topological strings on del Pezzo geometries, From quantum curves to topological string partition functions, Bootstrapping Calabi–Yau quantum mechanics, Quantum curves from refined topological recursion: the genus 0 case, 40 bilinear relations of \(q\)-Painlevé VI from \(\mathcal{N} = 4\) super Chern-Simons theory, Exponential networks, WKB and topological string, Topological strings and Wilson loops, D-type minimal conformal matter: quantum curves, elliptic Garnier systems, and the 5d descendants, Localization at largeNin Chern–Simons-matter theories, Exact eigenfunctions and the open topological string, Spectral determinants and quantum theta functions, Thermal entropy in Calabi-Yau quantum mechanics, Quantum curves, resurgence and exact WKB, Holomorphic anomaly and quantum mechanics, Resurgence matches quantization, Spectral theory and mirror symmetry, On the Gopakumar–Ooguri–Vafa correspondence for Clifford–Klein 3-manifolds, Singular vector structure of quantum curves, Exact quantization conditions for cluster integrable systems, Gauge/Vortex Duality and AGT, B-Model Approach to Instanton Counting, The complex side of the TS/ST correspondence, Hofstadter’s butterfly in quantum geometry, A-Polynomial, B-Model, and Quantization, Quantum mirror map for del Pezzo geometries, Intersecting defects and supergroup gauge theory

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Loop and surface operators in \( \mathcal{N} = 2 \) gauge theory and Liouville modular geometry
• Nekrasov functions and exact Bohr-Sommerfeld integrals
• Topological expansion of the \(\beta\)-ensemble model and quantum algebraic geometry in the sectorwise approach
• Resolvents and Seiberg-Witten representation for a Gaussian \(\beta\)-ensemble
• Vortex counting and Lagrangian 3-manifolds
• Surface operator, bubbling Calabi-Yau and AGT relation
• A new 2d/4d duality via integrability
• Non-perturbative topological strings and conformal blocks
• Quantization of integrable systems and a \(2d/4d\) duality
• On AGT relations with surface operator insertion and a stationary limit of beta-ensembles
• Wall crossing and M-theory
• Extended holomorphic anomaly in gauge theory
• Deformed prepotential, quantum integrable system and Liouville field theory
• Hermitian matrix model free energy: Feynman graph technique for all genera
• Matrix eigenvalue model: Feynman graph technique for all genera
• Quantization of the Hitchin moduli spaces, Liouville theory and the geometric Langlands correspondence. I
• Seiberg-Witten prepotential from instanton counting
• Affine \(SL(2)\) conformal blocks from 4d gauge theories
• Topological strings and integrable hierarchies
• Higgs bundles, gauge theories and quantum groups
• Laumon spaces and the Calogero-Sutherland integrable system
• Infinite conformal symmetry in two-dimensional quantum field theory
• Kodaira-Spencer theory of gravity and exact results for quantum string amplitudes
• Riemann surfaces, separation of variables and classical and quantum integrability
• Matrix models, topological strings, and supersymmetric gauge theories
• Integrating over Higgs branches
• The matrix model version of AGT conjecture and CIV-DV prepotential
• A \& B model approaches to surface operators and Toda thoeries
• The omega deformation, branes, integrability and Liouville theory
• Split states, entropy enigmas, holes and halos
• Khovanov-Rozansky homology and topological strings
• \(\text{SU}(N)\) geometries and topological string amplitudes
• The topological vertex
• Perturbative analysis of gauged matrix models
• Quantum Integrability and Supersymmetric Vacua
• Nekrasov functions from exact Bohr–Sommerfeld periods: the case ofSU(N)
• An Ar threesome: Matrix models, 2d conformal field theories, and 4d N=2 gauge theories
• The uses of the refined matrix model recursion
• On the gauge theory/geometry correspondence
• Knot invariants and topological strings.
• A large \(N\) duality via a geometric transition