Quantum Foam and Topological Strings

Abstract

We find an interpretation of the recent connection found between topological strings on Calabi-Yau threefolds and crystal melting: Summing over statistical mechanical configuration of melting crystal is equivalent to a quantum gravitational path integral involving fluctuations of Kahler geometry and topology. We show how the limit shape of the melting crystal emerges as the average geometry and topology of the quantum foam at the string scale. The geometry is classical at large length scales, modified to a smooth limit shape dictated by mirror geometry at string scale and is a quantum foam at area scales g_s α'.

55 pages

References in corpus (27)

• String Theory and Noncommutative Geometry
• Phases of $N=2$ Theories In Two Dimensions
• Kodaira-Spencer Theory of Gravity and Exact Results for Quantum String Amplitudes
• A Strong Coupling Test of S-Duality
• D-Branes and Topological Field Theories
• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Instantons on noncommutative R^4, and (2,0) superconformal six dimensional theory
• Knot Invariants and Topological Strings
• D-Branes And Mirror Symmetry
• Integrating Over Higgs Branches
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• D-particle bound states and generalized instantons
• Topological Amplitudes in String Theory
• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• Lectures on Loop Quantum Gravity
• Branes and N=2 Theories in Two Dimensions
• Special Quantum Field Theories In Eight And Other Dimensions
• Euclidean SYM Theories by Time Reduction and Special Holonomy Manifolds
• Higher Dimensional Analogues of Donaldson-Witten Theory
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• Theory of Kähler Gravity
• Space-Time Foam From Non-Commutative Instantons
• Non-Commutative Instantons and the Seiberg-Witten Map
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• Noncommutative instantons revisited
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Cited by in corpus (178)

• Black Hole Attractors and the Topological String
• Supergravity Microstates for BPS Black Holes and Black Rings
• Bubbling Supertubes and Foaming Black Holes
• Dimer models and toric diagrams
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• Dual geometries for a set of 3-charge microstates
• Chern-Simons Theory and Topological Strings
• D-brane Deconstructions in IIB Orientifolds
• The Library of Babel: On the origin of gravitational thermodynamics
• Refined, Motivic, and Quantum
• Euclidean wormholes, baby universes, and their impact on particle physics and cosmology
• Quantum W-symmetry in AdS_3
• S-duality and Topological Strings
• Crystal Melting and Toric Calabi-Yau Manifolds
• Emergent Gravity from Noncommutative Spacetime
• Explicit examples of DIM constraints for network matrix models
• Lectures on AdS Black Holes, Holography and Localization
• N=2 strings and the twistorial Calabi-Yau
• The String Landscape, the Swampland, and the Missing Corner
• Wall crossing in local Calabi Yau manifolds
• M-theory and a Topological String Duality
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• Topological wave functions and heat equations
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Cohomological gauge theory, quiver matrix models and Donaldson-Thomas theory
• A Geometric Look on the Microstates of Supertubes
• Quiver Yangian from Crystal Melting
• Derivation of Calabi-Yau Crystals from Chern-Simons Gauge Theory
• Wall Crossing and M-theory
• Refined Chern-Simons Theory and Topological String
• Magnificent Four with Colors
• Relating Field Theories via Stochastic Quantization
• Exploring ${\mathcal{W}}_{\infty }$ in the quadratic basis
• Quiver Yangian and Supersymmetric Quantum Mechanics
• On Exceptional Instanton Strings
• G2 Dualities in D=5 Supergravity and Black Strings
• Brownian Motion, Chern-Simons Theory, and 2d Yang-Mills
• Moduli of ADHM Sheaves and Local Donaldson-Thomas Theory
• Bound state transformation walls
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Instantons on ALE spaces and orbifold partitions
• Space-Time Foam From Non-Commutative Instantons
• Intersecting Solitons, Amoeba and Tropical Geometry
• UV Completions for Non-Critical Strings
• Wall Crossing, Quivers and Crystals
• Toroidal and Elliptic Quiver BPS Algebras and Beyond
• Five-Dimensional Supersymmetric Yang-Mills Theories and Random Plane Partitions
• Gauge theory, topological strings, and S-duality
• Spectral duality in elliptic systems, six-dimensional gauge theories and topological strings
• Quiver Matrix Model and Topological Partition Function in Six Dimensions
• D-branes as a Bubbling Calabi-Yau
• Evidence for F(uzz) Theory
• Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
• Superposition induced topology changes in quantum gravity
• Wall-crossing, free fermions and crystal melting
• Gauge/Bethe correspondence from quiver BPS algebras
• Topological strings and their physical applications
• On the Regularized Fermionic Projector of the Vacuum
• The Stringy Instanton Partition Function
• Crystal Melting and Black Holes
• D-branes as Defects in the Calabi-Yau Crystal
• Crystal Model for the Closed Topological Vertex Geometry
• Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
• Matrix Models and D-branes in Twistor String Theory
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Refined Black Hole Ensembles and Topological Strings
• Quantum Crystals and Spin Chains
• Open G2 Strings
• Amoebas and Instantons
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• q-deformations of two-dimensional Yang-Mills theory: Classification, categorification and refinement
• Topological Symmetry of forms, N=1 Supersymmetry and S-duality on Special Manifolds
• Random surfaces enumerating algebraic curves
• Crystal melting on toric surfaces
• Typicality, Black Hole Microstates and Superconformal Field Theories
• BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
• Instantons, Twistors, and Emergent Gravity
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• dS${}_2$ Supergravity
• D-Brane Amplitudes in Topological String on Conifold
• Cauchy formula and the character ring
• 7D supersymmetric Yang-Mills on curved manifolds
• Cobordism invariants from BPS q-series
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• Quiver Yangians and Crystal Melting: A Concise Summary
• Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
• Statistical model and BPS D4-D2-D0 counting
• Crystals and intersecting branes
• The elliptic genus from split flows and Donaldson-Thomas invariants
• Tetrahedron instantons
• Topological Quiver Matrix Models and Quantum Foam
• Correlators of Matrix Models on Homogeneous Spaces
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• Master Space and Hilbert Series for N=1 Field Theories
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• Playing with the index of M-theory
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• The Hodge-elliptic genus, spinning BPS states, and black holes
• The emergence of noncommutative target space in noncritical string theory
• G2 Hitchin functionals at one loop
• Gauge origami and quiver W-algebras
• Wall Crossing Phenomenology of Orientifolds
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Check-Operators and Quantum Spectral Curves
• Gravitational Quantum Foam and Supersymmetric Gauge Theories
• Crystal Melting, BPS Quivers and Plethystics
• Gauge Theories as String Theories: the First Results
• Mirror Symmetry in Emergent Gravity
• Toric Geometry and String Theory
• A note on statistical model for BPS D4-D2-D0 states
• Topological M Theory from Pure Spinor Formalism
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• One-loop derivation of the Wilson polygon - MHV amplitude duality
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• More on Affine Dynkin Quiver Yangians
• Noncommutative Instantons in Diverse Dimensions
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• The Spectra of Supersymmetric States in String Theory
• Wall-Crossing Effects on Quiver BPS Algebras
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?
• Charging solid partitions
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Instanton Counting and Dielectric Branes
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• Lectures in Quantum Gravity
• D-branes Wrapped on Fuzzy del Pezzo Surfaces
• Statistics of close-packed dimers on fractal lattices
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Quantum crystals, Kagome lattice and plane partitions fermion-boson duality
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• Quantized Kähler Geometry and Quantum Gravity
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• On Framed Quivers, BPS Invariants and Defects
• Baby Universes born from the Void
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• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
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• BPS states, crystals and matrices
• Open-Closed String Duality from Orbifolded Conifolds
• Dimer Models, Free Fermions and Super Quantum Mechanics
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• q-Deformed Oscillators and D-branes on Conifold
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• Towards The Moduli Space of Extended Partial Isometries
• Stringy phenomenology with preon models
• Charge functions for odd dimensional partitions
• Strings, Integrable Systems, Geometry and Statistical Models
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• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
• M theory and the Coulomb phase of higher rank DT invariants
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• Twistor Spaces, Mirror Symmetry and Self-dual Kahler Manifolds
• Supersymmetric Gauge Theories with Matters, Toric Geometries and Random Partitions
• Shifts of prepotentials (with an appendix by Michele Vergne)
• Geometry As Seen By String Theory
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• A question on generalization of partition functions of CY 3-folds in String Theory
• Gauge theories with 16 supersymmetries on spheres
• Topological Heterotic Rings
• The DT-instanton equation on almost Hermitian 6-manifolds