Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I

Abstract

We study BPS spectra of D-branes on local Calabi-Yau threefolds $\mathcal{O}(-p)\oplus \mathcal{O}(p-2)\to {\mathbb{P}}^1$ with $p=0,1$, corresponding to ${\mathbb{C}}^3/{\mathbb{Z}}_2$ and the resolved conifold. Nonabelianization for exponential networks is applied to compute directly unframed BPS indices counting states with D2 and D0 brane charges. Known results on these BPS spectra are correctly reproduced by computing new types of BPS invariants of 3d-5d BPS states, encoded by nonabelianization, through their wall-crossing. We also develop the notion of exponential BPS graphs for the simplest toric examples, and show that they encode both the quiver and the potential associated to the Calabi-Yau via geometric engineering.

arXiv comment52+4 pages

References in corpus (80)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Phases of $N=2$ Theories In Two Dimensions
• N=2 dualities
• Solutions Of Four-Dimensional Field Theories Via M Theory
• Superconformal Field Theory on Threebranes at a Calabi-Yau Singularity
• Stability structures, motivic Donaldson-Thomas invariants and cluster transformations
• Black Hole Entropy in M-Theory
• Geometric Engineering of Quantum Field Theories
• Four-dimensional wall-crossing via three-dimensional field theory
• The Refined Topological Vertex
• Extremal Transitions and Five-Dimensional Supersymmetric Field Theories
• Loop and surface operators in N=2 gauge theory and Liouville modular geometry
• On Classification of N=2 Supersymmetric Theories, (e-mail uncorrupted version)
• D-Branes And Mirror Symmetry
• Mock Theta Functions
• Self-Dual Strings and N=2 Supersymmetric Field Theory
• Mirror Symmetry, D-Branes and Counting Holomorphic Discs
• Statistical Entropy of Four-Dimensional Extremal Black Holes
• Vortex Counting and Lagrangian 3-manifolds
• A New Supersymmetric Index
• Disk Instantons, Mirror Symmetry and the Duality Web
• Split States, Entropy Enigmas, Holes and Halos
• Non-perturbative effects and the refined topological string
• The spectrum of BPS branes on a noncompact Calabi-Yau
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Spectral networks
• Wall-Crossing from Boltzmann Black Hole Halos
• A Farey Tail for Attractor Black Holes
• Wall-Crossing in Coupled 2d-4d Systems
• Surface Operators in N=2 4d Gauge Theories
• Non-commutative Donaldson-Thomas theory and the conifold
• N=2 Quantum Field Theories and Their BPS Quivers
• Computation of Superpotentials for D-Branes
• Surface Defects and Resolvents
• D-instantons and twistors
• BPS states and algebras from quivers
• A fixed point formula for the index of multi-centered N=2 black holes
• Wall crossing in local Calabi Yau manifolds
• Relative Lefschetz Action and BPS State Counting
• From Black Holes to Quivers
• BPS States and Minimal Surfaces
• Non-perturbative approaches to the quantum Seiberg-Witten curve
• Brane Brick Models in the Mirror
• Seiberg-Witten theory and matrix models
• Wild Wall Crossing and BPS Giants
• tt* Geometry in 3 and 4 Dimensions
• Vafa-Witten invariants for projective surfaces I: stable case
• On the Coulomb and Higgs branch formulae for multi-centered black holes and quiver invariants
• Vafa-Witten invariants for projective surfaces II: semistable case
• Topological Strings, D-Model, and Knot Contact Homology
• Multiple D3-instantons and mock modular forms I
• Indefinite theta series and generalized error functions
• Algebra of the Infrared: String Field Theoretic Structures in Massive $\mathcal{N}=(2,2)$ Field Theory In Two Dimensions
• Equivariant K-theory and refined Vafa-Witten invariants
• Vafa-Witten invariants from exceptional collections
• Exponential Networks and Representations of Quivers
• Attractor flow trees, BPS indices and quivers
• Exploring 5d BPS Spectra with Exponential Networks
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Virtual refinements of the Vafa-Witten formula
• Gromov-Witten/Donaldson-Thomas correspondence for toric 3-folds
• S-duality and refined BPS indices
• BPS Graphs: From Spectral Networks to BPS Quivers
• Computing a pyramid partition generating function with dimer shuffling
• N=4 Supersymmetric Yang-Mills Theory on a Kaehler Surface
• Wall-crossing of D4-D2-D0 and flop of the conifold
• Instantons, Quivers and Noncommutative Donaldson-Thomas Theory
• Surface operators, chiral rings, and localization in N=2 gauge theories
• Invariants of moduli spaces of stable sheaves on ruled surfaces
• BPS invariants of N=4 gauge theory on a surface
• Topological recursion and mirror curves
• The quiver approach to the BPS spectrum of a 4d N=2 gauge theory
• Vafa-Witten invariants from modular anomaly
• Rank $N$ Vafa-Witten invariants, modularity and blow-up
• ADE Spectral Networks and Decoupling Limits of Surface Defects
• Surface operators in 5d gauge theories and duality relations
• More about vanishing cycles and mutation
• $Y$ systems, $Q$ systems, and 4D $\mathcal{N}=2$ supersymmetric QFT
• Dimer models for parallelograms
• Categorical Wall-Crossing in Landau-Ginzburg Models

Cited by in corpus (10)

• Peacock patterns and new integer invariants in topological string theory
• Exact WKB methods in $SU(2)$ $N_f=1$
• Exponential BPS graphs and D brane counting on toric Calabi-Yau threefolds: Part I
• Mathematical structures of non-perturbative topological string theory: from GW to DT invariants
• Exponential Networks, WKB and Topological String
• On the BPS spectrum of 5d SU(2) super-Yang-Mills
• 5D BPS Quivers and KK Towers
• A-branes, foliations and localization
• The $U$-plane of rank-one 4d $\mathcal{N}=2$ KK theories
• Attractor invariants, brane tilings and crystals