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 (5)

• The Topological Vertex
• Topological Strings and Integrable Hierarchies
• Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
• N=1 Supersymmetry, Deconstruction, and Bosonic Gauge Theories
• On the Worldsheet Derivation of Large N Dualities for the Superstring

Cited by in corpus (177)

• 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
• Split States, Entropy Enigmas, Holes and Halos
• 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
• Wall Crossing of BPS States on the Conifold from Seiberg Duality and Pyramid Partitions
• 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
• Relating Field Theories via Stochastic Quantization
• Magnificent Four with Colors
• 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
• Toric Calabi-Yau threefolds as quantum integrable systems. R-matrix and RTT relations
• Bound state transformation walls
• Instantons on ALE spaces and orbifold partitions
• 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
• Wall-crossing, free fermions and crystal melting
• Superposition induced topology changes in quantum gravity
• Deformed boson-fermion correspondence, Q-bosons, and topological strings on the conifold
• Topological strings and their physical applications
• Gauge/Bethe correspondence from quiver BPS algebras
• On the Regularized Fermionic Projector of the Vacuum
• The Stringy Instanton Partition Function
• D-branes as Defects in the Calabi-Yau Crystal
• Crystal Melting and Black Holes
• Matrix Models and D-branes in Twistor String Theory
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Crystal Model for the Closed Topological Vertex Geometry
• Self-Organized Criticality and Pattern Emergence through the lens of Tropical Geometry
• Refined Black Hole Ensembles and Topological Strings
• Quantum Crystals and Spin Chains
• Open G2 Strings
• Amoebas and Instantons
• 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
• Two-dimensional crystal melting and D4-D2-D0 on toric Calabi-Yau singularities
• Crystal melting on toric surfaces
• Typicality, Black Hole Microstates and Superconformal Field Theories
• dS${}_2$ Supergravity
• Instantons, Twistors, and Emergent Gravity
• ADHM in 8d, coloured solid partitions and Donaldson-Thomas invariants on orbifolds
• BPS State Counting in Local Obstructed Curves from Quiver Theory and Seiberg Duality
• D-Brane Amplitudes in Topological String on Conifold
• Cauchy formula and the character ring
• 7D supersymmetric Yang-Mills on curved manifolds
• Statistical model and BPS D4-D2-D0 counting
• Quiver Yangians and Crystal Melting: A Concise Summary
• Cobordism invariants from BPS q-series
• Crystals and intersecting branes
• Cohomological Hall algebras and perverse coherent sheaves on toric Calabi-Yau 3-folds
• Generalized MacMahon G(q) as q-deformed CFT Correlation Function
• The elliptic genus from split flows and Donaldson-Thomas invariants
• Correlators of Matrix Models on Homogeneous Spaces
• Topological Quiver Matrix Models and Quantum Foam
• Special Geometry and Mirror Symmetry for Open String Backgrounds with N=1 Supersymmetry
• Tetrahedron instantons
• N=2 gauge theories, instanton moduli spaces and geometric representation theory
• Graded Quivers, Generalized Dimer Models and Toric Geometry
• Master Space and Hilbert Series for N=1 Field Theories
• A Note on Quiver Yangians and $\mathcal{R}$-Matrices
• Playing with the index of M-theory
• The emergence of noncommutative target space in noncritical string theory
• The Hodge-elliptic genus, spinning BPS states, and black holes
• G2 Hitchin functionals at one loop
• Thermodynamics of Noncritical M-Theory and the Topological A-Model
• Wall Crossing Phenomenology of Orientifolds
• Gauge origami and quiver W-algebras
• Toric Geometry and String Theory
• Gauge Theories as String Theories: the First Results
• Gravitational Quantum Foam and Supersymmetric Gauge Theories
• Crystal Melting, BPS Quivers and Plethystics
• A note on statistical model for BPS D4-D2-D0 states
• Check-Operators and Quantum Spectral Curves
• Contravariant Gravity on Poisson Manifolds and Einstein Gravity
• Mirror Symmetry in Emergent Gravity
• More on Affine Dynkin Quiver Yangians
• Topological M Theory from Pure Spinor Formalism
• Aspects of Twistor Geometry and Supersymmetric Field Theories within Superstring Theory
• Asymptotic safety, quantum gravity, and the swampland: a conceptual assessment
• Quiver Yangians and $\mathcal{W}$-Algebras for Generalized Conifolds
• Noncommutative Instantons in Diverse Dimensions
• Refined toric branes, surface operators and factorization of generalized Macdonald polynomials
• Amplitudes in the N=4 SYM from Quantum Geometry of the Momentum Space
• One-loop derivation of the Wilson polygon - MHV amplitude duality
• The Spectra of Supersymmetric States in String Theory
• Wall-Crossing Effects on Quiver BPS Algebras
• Charging solid partitions
• Evidence for an Algebra of ${\mathbf{G}}_2$ Instantons
• On the M2-Brane Index on Noncommutative Crepant Resolutions
• Cut-and-join operators and Macdonald polynomials from the 3-Schur functions
• Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?
• Instanton Counting and Dielectric Branes
• Lectures in Quantum Gravity
• Matrix models and stochastic growth in Donaldson-Thomas theory
• Localization on the D-brane, two-dimensional gauge theory and matrix models
• Baby Universes born from the Void
• Quantum Black Hole Entropy, Localization and the Stringy Exclusion Principle
• Reconstructing GKZ via topological recursion
• Quantized Kähler Geometry and Quantum Gravity
• Statistics of close-packed dimers on fractal lattices
• Quantum crystals, Kagome lattice and plane partitions fermion-boson duality
• Gauge origami and quiver W-algebras III: Donaldson--Thomas $qq$-characters
• On Framed Quivers, BPS Invariants and Defects
• D-branes Wrapped on Fuzzy del Pezzo Surfaces
• BPS states, crystals and matrices
• Topological Strings, Two-Dimensional Yang-Mills Theory and Chern-Simons Theory on Torus Bundles
• Open-Closed String Duality from Orbifolded Conifolds
• Crystals and Double Quiver Algebras from Jeffrey-Kirwan Residues
• Mahler Measure for a Quiver Symphony
• Seven-dimensional super Yang-Mills at negative coupling
• q-Deformed Oscillators and D-branes on Conifold
• Attractor invariants, brane tilings and crystals
• Spacetime foam in twistor string theory
• Dimer Models, Free Fermions and Super Quantum Mechanics
• Topological strings live on attractive manifolds
• Black holes and balanced metrics
• Mellin-Barnes Representation of the Topological String
• Topological Gauge Theories on Local Spaces and Black Hole Entropy Countings
• BPS Spectra, Barcodes and Walls
• Geometry and Combinatorics of Crystal Melting
• Generalized q-deformed Correlation Functions as Spectral Functions of Hyperbolic Geometry
• M theory and the Coulomb phase of higher rank DT invariants
• Refined Wall-Crossing, Free Fermions and Crystal Melting
• Hermitian-Einstein metrics from noncommutative $U\left(1\right)$ instantons
• Dimensional Reduction of Seiberg-Witten Monopole Equations, N=2 Noncommutative Supersymmetric Field Theories and Young Diagrams
• Charge functions for odd dimensional partitions
• U-duality Invariant Quantum Entropy from Sums of Kloosterman Sums
• Strings, Integrable Systems, Geometry and Statistical Models
• Szasz Analytic Functions and Noncompact Kähler Toric Manifolds
• Some comments on the local curve (B-side)
• Stringy phenomenology with preon models
• Towards The Moduli Space of Extended Partial Isometries
• A question on generalization of partition functions of CY 3-folds in String Theory
• Topological string amplitudes and Seiberg-Witten prepotentials from the counting of dimers in transverse flux
• Geometry As Seen By String Theory
• The DT-instanton equation on almost Hermitian 6-manifolds
• Gauge theories with 16 supersymmetries on spheres
• 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)
• Topological Heterotic Rings