Refined stable pair invariants for E-, M- and [p,q]-strings

Abstract

We use mirror symmetry, the refined holomorphic anomaly equation and modularity properties of elliptic singularities to calculate the refined BPS invariants of stable pairs on non-compact Calabi-Yau manifolds, based on del Pezzo surfaces and elliptic surfaces, in particular the half K3. The BPS numbers contribute naturally to the five-dimensional N=1 supersymmetric index of M-theory, but they can be also interpreted in terms of the superconformal index in six dimensions and upon dimensional reduction the generating functions count N=2 Seiberg-Witten gauge theory instantons in four dimensions. Using the M/F-theory uplift the additional information encoded in the spin content can be used in an essential way to obtain information about BPS states in physical systems associated to small instantons, tensionless strings, gauge symmetry enhancement in F-theory by [p,q]-strings as well as M-strings.

120 pages, 21 figures

References in corpus (15)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• The Refined Topological Vertex
• Webs of five-branes and N=2 superconformal field theories
• Open string amplitudes and large order behavior in topological string theory
• Non-perturbative effects and the refined topological string
• Remodeling the B-model
• Chiral Four-Dimensional F-Theory Compactifications With SU(5) and Multiple U(1)-Factors
• Extended Holomorphic Anomaly in Gauge Theory
• Holomorphic Anomaly in Gauge Theories and Matrix Models
• Refined Chern-Simons Theory and Topological String
• Shift versus Extension in Refined Partition Functions
• The refined BPS index from stable pair invariants
• Direct integration for general Omega backgrounds
• Weak Coupling, Degeneration and Log Calabi-Yau Spaces
• Counting BPS States via Holomorphic Anomaly Equations

Cited by in corpus (90)

• Tensionless Strings and the Weak Gravity Conjecture
• F-Theory on all Toric Hypersurface Fibrations and its Higgs Branches
• 5d Superconformal Field Theories and Graphs
• Fibers add Flavor, Part I: Classification of 5d SCFTs, Flavor Symmetries and BPS States
• Non-Lagrangian Theories from Brane Junctions
• Strings of Minimal 6d SCFTs
• Elliptic Fibrations with Rank Three Mordell-Weil Group: F-theory with U(1) x U(1) x U(1) Gauge Symmetry
• Matrix models from operators and topological strings, 2
• Elliptic Genus of E-strings
• New Exact Quantization Condition for Toric Calabi-Yau Geometries
• Seiberg-Witten theory as a Fermi gas
• Operators from mirror curves and the quantum dilogarithm
• The $l$-loop Banana Amplitude from GKZ Systems and relative Calabi-Yau Periods
• Matrix models from operators and topological strings
• Refined BPS invariants of 6d SCFTs from anomalies and modularity
• Topological Strings and Quantum Spectral Problems
• Topological Strings on Singular Elliptic Calabi-Yau 3-folds and Minimal 6d SCFTs
• Tao Probing the End of the World
• Exact quantization conditions for the relativistic Toda lattice
• E + E $\to$ H
• Quantum geometry of del Pezzo surfaces in the Nekrasov-Shatashvili limit
• Exact quantization conditions for cluster integrable systems
• Exact Instanton Expansion of Superconformal Chern-Simons Theories from Topological Strings
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Peacock patterns and new integer invariants in topological string theory
• Elliptic Blowup Equations for 6d SCFTs. II: Exceptional Cases
• Operators and higher genus mirror curves
• 5d $E_n$ Seiberg-Witten curve via toric-like diagram
• Resurgence Matches Quantization
• Complete prepotential for 5d $\mathcal{N}=1$ superconformal field theories
• Blowup Equations for Refined Topological Strings
• A Solvable Deformation of Quantum Mechanics
• Discrete theta angle from an O5-plane
• Elliptic Blowup Equations for 6d SCFTs. III: E-strings, M-strings and Chains
• Exact Quantization Conditions, Toric Calabi-Yau and Nonperturbative Topological String
• S-duality and refined BPS indices
• Discrete Symmetries in Heterotic/F-theory Duality and Mirror Symmetry
• Exact multi-instantons in topological string theory
• Exact eigenfunctions and the open topological string
• Instanton Effects in Rank Deformed Superconformal Chern-Simons Theories from Topological Strings
• The Cremmer-Scherk Mechanism in F-theory Compactifications on K3 Manifolds
• On the resurgent structure of quantum periods
• Calabi-Yau geometry and electrons on 2d lattices
• BPS relations from spectral problems and blowup equations
• Superconformal Chern-Simons Theories from del Pezzo Geometries
• On the Elliptic Genus of Three E-strings and Heterotic Strings
• Comparing elliptic and toric hypersurface Calabi-Yau threefolds at large Hodge numbers
• Comments on Exact Quantization Conditions and Non-Perturbative Topological Strings
• Symmetry Breaking in Quantum Curves and Super Chern-Simons Matrix Models
• Modular Anomaly Equation for Schur Index of $\mathcal{N}=4$ Super-Yang-Mills
• Elliptic Blowup Equations for 6d SCFTs. IV: Matters
• Modular curves, the Tate-Shafarevich group and Gopakumar-Vafa invariants with discrete charges
• Spectral Theories and Topological Strings on del Pezzo Geometries
• Quasi-Jacobi Forms, Elliptic Genera and Strings in Four Dimensions
• Large N non-perturbative effects in $\mathcal{N}=4$ superconformal Chern-Simons theories
• Hofstadter's Butterfly and Langlands Duality
• A Note on Instanton Effects in ABJM Theory
• Hanany-Witten Transition in Quantum Curves
• Computing the elliptic genus of higher rank E-strings from genus 0 GW invariants
• BPS states in the Minahan-Nemeschansky E6 theory
• Spectral determinants and quantum theta functions
• Reading between the rational sections: Global structures of 4d $\mathcal{N}=2$ KK theories
• Topological strings and Wilson loops
• Quantum Hall Effect and Langlands Program
• Seiberg-Witten curves with O7${}^{\pm }$-planes
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Resonances and PT symmetry in quantum curves
• A reduced BPS index of E-strings
• Thermodynamic limit of the Nekrasov-type formula for E-string theory
• On finiteness of Type IIB compactifications: Magnetized branes on elliptic Calabi-Yau threefolds
• Towards Refining the Topological Strings on Compact Calabi-Yau 3-folds
• Brane Transitions from Exceptional Groups
• Quantum Periods and Spectra in Dimer Models and Calabi-Yau Geometries
• Dessins d'Enfants, Seiberg-Witten Curves and Conformal Blocks
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Bootstrapping ADE M-strings
• Large N instantons from topological strings
• Log BPS numbers of log Calabi-Yau surfaces
• Duality Cascades and Affine Weyl Groups
• Exact solutions to quantum spectral curves by topological string theory
• E-strings, $F_4$, and $D_4$ triality
• Coulomb branch surgery: Holonomy saddles, S-folds and discrete symmetry gaugings
• Resurgence, Stokes constants, and arithmetic functions in topological string theory
• Refined BPS numbers on compact Calabi-Yau threefolds from Wilson loops
• Recent Developments in Topological String Theory
• Algebraic construction of Weyl invariant $E_8$ Jacobi forms
• State counting on fibered CY-3 folds and the non-Abelian Weak Gravity Conjecture
• Topological String on elliptic CY 3-folds and the ring of Jacobi forms
• Seiberg-Witten geometry, modular rational elliptic surfaces and BPS quivers
• Quantum Mirror Map for Del Pezzo Geometries