Partition functions of N=(2,2) gauge theories on S^2 and vortices

Abstract

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet-Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. As applications we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.

62 pages + 16 of appendices; v2: minor modifications, refs added; v3: typos corrected, ref added

References in corpus (61)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Liouville Correlation Functions from Four-dimensional Gauge Theories
• N=2 dualities
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Type IIB Superstrings, BPS Monopoles, And Three-Dimensional Gauge Dynamics
• The Exact Superconformal R-Symmetry Extremizes Z
• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Mirror Manifolds And Topological Field Theory
• Notes on SUSY Gauge Theories on Three-Sphere
• Integrating Over Higgs Branches
• Wall-crossing, Hitchin Systems, and the WKB Approximation
• D-particle bound states and generalized instantons
• The complete superconformal index for N=6 Chern-Simons theory
• Exact Results in D=2 Supersymmetric Gauge Theories
• Vortex Counting and Lagrangian 3-manifolds
• Webs of five-branes and N=2 superconformal field theories
• Index for three dimensional superconformal field theories with general R-charge assignments
• Four-Dimensional SCFTs from M5-Branes
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
• Comments on 3d Seiberg-like dualities
• Black Holes, q-Deformed 2d Yang-Mills, and Non-perturbative Topological Strings
• Moduli Space of Non-Abelian Vortices
• Topological Reduction of 4D SYM to 2D $\sigma$--Models
• Mirrors of 3d Sicilian theories
• A Construction of Killing Spinors on S^n
• Tinkertoys for Gaiotto Duality
• Branes and N=2 Theories in Two Dimensions
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Supersymmetric Gauge Theories on the Five-Sphere
• Sicilian gauge theories and N=1 dualities
• 4d Index to 3d Index and 2d TQFT
• Factorisation of N = 2 theories on the squashed 3-sphere
• Correlation functions in conformal Toda field theory I
• TASI Lectures on Solitons
• On The Conformal Field Theory Of The Higgs Branch
• Generalized Superconformal Index for Three Dimensional Field Theories
• Para-Liouville/Toda central charges from M5-branes
• Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
• Seiberg-Witten Theory and Random Partitions
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Exact Results for 't Hooft Loops in Gauge Theories on S^4
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• AdS/CFT Dual Pairs from M5-Branes on Riemann Surfaces
• Vertices, Vortices & Interacting Surface Operators
• Liouville/Toda central charges from M5-branes
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• The large N limit of M2-branes on Lens spaces
• Line operators on S^1xR^3 and quantization of the Hitchin moduli space
• 3-Manifolds and 3d Indices
• Seiberg-Witten prepotential from instanton counting
• On F-term contribution to effective action
• Mirror Symmetry in 2+1 and 1+1 Dimensions
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Gauge Theories Labelled by Three-Manifolds
• Tools for supersymmetry
• Vortex counting from field theory
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• N=4 Versus N=2 Phases, HyperkÄhler Quotients and the 2D Topological Twist

Cited by in corpus (222)

• Elliptic genera of 2d N=2 gauge theories
• Exact Results in D=2 Supersymmetric Gauge Theories
• A topologically twisted index for three-dimensional supersymmetric theories
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• Two-dimensional SCFTs from wrapped branes and c-extremization
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• Supersymmetry on Curved Spaces and Holography
• Comments on twisted indices in 3d supersymmetric gauge theories
• Sphere Partition Functions and the Zamolodchikov Metric
• Correlation Functions of Coulomb Branch Operators
• Black holes in 4d $\mathcal{N}=4$ Super-Yang-Mills
• Anomalies, Conformal Manifolds, and Spheres
• The Refined Swampland Distance Conjecture in Calabi-Yau Moduli Spaces
• Higgs branch localization in three dimensions
• Supersymmetric partition functions and the three-dimensional A-twist
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Instantons on the 5-sphere and M5-branes
• Exact Results In Two-Dimensional (2,2) Supersymmetric Gauge Theories With Boundary
• Feynman Integrals in Dimensional Regularization and Extensions of Calabi-Yau Motives
• 3d Chern-Simons Theory from M5-branes
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• 5D partition functions, q-Virasoro systems and integrable spin-chains
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• M2-brane surface operators and gauge theory dualities in Toda
• Higgs branch localization of 3d N=2 theories
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Factorisation and holomorphic blocks in 4d
• Vortex partition functions, wall crossing and equivariant Gromov-Witten invariants
• Cluster algebras from dualities of 2d N=(2,2) quiver gauge theories
• Wilson lines as superconformal defects in ABJM theory: a formula for the emitted radiation
• A Bethe Ansatz type formula for the superconformal index
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Localization on three-dimensional manifolds
• F-theory and AdS_3/CFT_2 (2,0)
• Rotating Black Hole Entropy from M5-branes
• Supersymmetric partition functions on Riemann surfaces
• New Methods for Characterizing Phases of 2D Supersymmetric Gauge Theories
• Perturbative Corrections to Kahler Moduli Spaces
• Localization and AdS/CFT Correspondence
• Landscaping with fluxes and the E8 Yukawa Point in F-theory
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$
• Kahler Potential and Ambiguities in 4d N=2 SCFTs
• Special Points of Inflation in Flux Compactifications
• The grin of Cheshire cat resurgence from supersymmetric localization
• Central Charges of 2d Superconformal Defects
• On Supersymmetric Gauge Theories on S^4 x S^1
• Undoing decomposition
• The long flow to freedom
• Schur correlation functions on $S^3\times S^1$
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• Six-dimensional supersymmetric gauge theories, quantum cohomology of instanton moduli spaces and gl(N) Quantum Intermediate Long Wave Hydrodynamics
• Holomorphic blocks and the 5d AGT correspondence
• A slow review of the AGT correspondence
• Intersecting Surface Defects and Two-Dimensional CFT
• Predictions for Gromov-Witten invariants of noncommutative resolutions
• Intersecting Surface Defects and Instanton Partition Functions
• Notes on nonabelian (0,2) theories and dualities
• Refined swampland distance conjecture and exotic hybrid Calabi-Yaus
• Surface defects and instanton-vortex interaction
• Decomposition in diverse dimensions
• Quantum periods of Calabi-Yau fourfolds
• Sigma Models on Flags
• A proposal for nonabelian (0,2) mirrors
• Chiral Algebras, Localization and Surface Defects
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• From 3d duality to 2d duality
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Supersymmetric localization in two dimensions
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Introduction to localization in quantum field theory
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Localization of twisted $\mathcal{N}=(0,2)$ gauged linear sigma models in two dimensions
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Quiver gauge theories and integrable lattice models
• The Stringy Instanton Partition Function
• Shortening Anomalies in Supersymmetric Theories
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Two-Sphere Partition Functions and Gromov-Witten Invariants
• Supersymmetric Liouville theory in AdS${}_2$ and AdS/CFT
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Integrability from 2d N=(2,2) Dualities
• Factorization of 4d N=1 superconformal index
• Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
• Exact Partition Functions on RP2 and Orientifolds
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Basic hypergeometry of supersymmetric dualities
• Supersymmetric index on T^2 x S^2 and elliptic genus
• Superspin chains from superstring theory
• 2d SCFTs from M2-branes
• N=2 SUSY gauge theories on S^4
• Ellipsoid partition function from Seiberg-Witten monopoles
• Dual Pairs of Gauged Linear Sigma Models and Derived Equivalences of Calabi-Yau threefolds
• A few Ricci-flat stacks as phases of exotic GLSM's
• Supersymmetric Yang-Mills, Spherical Branes, and Precision Holography
• Supersymmetric Rényi Entropy in Two Dimensions
• Quantum sheaf cohomology on Grassmannians
• Exact results for vortex loop operators in 3d supersymmetric theories
• On 3d Seiberg-like Dualities with Two Adjoints
• Localization on round sphere revisited
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Topological Correlators and Surface Defects from Equivariant Cohomology
• Superfield theories on $S^3$ and their localization
• Calabi's diastasis as interface entropy
• Quantum Cohomology and Quantum Hydrodynamics from Supersymmetric Quiver Gauge Theories
• Modular and duality properties of surface operators in N=2* gauge theories
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• Analytic continuation of dimensions in supersymmetric localization
• A-twisted correlators and Hori dualities
• Supersymmetric indices on $I\times T^2$, elliptic genera and dualities with boundaries
• dS${}_2$ Supergravity
• AGT/Z${}_2$
• New Supersymmetric Localizations from Topological Gravity
• Chiral operators in two-dimensional (0,2) theories and a test of triality
• 3d Expansions of 5d Instanton Partition Functions
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Supersymmetric vortex defects in two dimensions
• Exact results for boundaries and domain walls in 2d supersymmetric theories
• Factorisation of 3d $\mathcal{N}=4$ Twisted Indices and the Geometry of Vortex Moduli Space
• Factorising the 3D Topologically Twisted Index
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• SYM on Quotients of Spheres and Complex Projective Spaces
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• Integrable lattice spin models from supersymmetric dualities
• A proposal for (0,2) mirrors of toric varieties
• Connecting Mirror Symmetry in 3d and 2d via Localization
• Elliptic non-Abelian Donaldson-Thomas invariants of ${\mathbb{C}}^3$
• Semichiral Fields on S^2 and Generalized Kähler Geometry
• Mathematical structures behind supersymmetric dualities
• On Supersymmetry, Boundary Actions and Brane Charges
• Orbifolds, Defects and Sphere Partition Function
• Exact computation of the Special geometry for Calabi-Yau hypersurfaces of Fermat type
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Localization principle in SUSY gauge theories
• Localization of a supersymmetric gauge theory in the presence of a surface defect
• Vortex-Strings in N=2 SQCD and Bulk-String Decoupling
• JKLMR conjecture and Batyrev construction
• Bootstrapping the $S^5$ partition function
• $\mathcal{N}=2$ supersymmetric gauge theories on $S^2\times S^2$ and Liouville Gravity
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Gromov-Witten invariants and localization
• Linear Quivers at Large-$N$
• AGT relation in the light asymptotic limit
• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
• Semi-doubled Gauged Linear Sigma Model for Five-branes of Codimension Two
• Factorization of the 3d superconformal index
• Equivariant A-twisted GLSM and Gromov--Witten invariants of CY 3-folds in Grassmannians
• Gauge and matter superfield theories on $S^2$
• Lens partition function, pentagon identity and star-triangle relation
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• A few recent developments in 2d (2,2) and (0,2) theories
• Hemisphere Partition Function and Monodromy
• Ramond-Ramond couplings of D-branes
• On exact correlation functions of chiral ring operators in $2d$ $\mathcal{N}=(2,2)$ SCFTs via localization
• On genus one fibered Calabi-Yau threefolds with 5-sections
• Partition functions of $\mathcal{N}=(2,2)$ supersymmetric sigma models and Special geometry for the two-moduli non-Fermat Calabi-Yau manifold
• Remarks on 2d Unframed Quiver Gauge Theories
• Higgs and Coulomb Branch Descriptions of the Volume of the Vortex Moduli Space
• Local B-model Yukawa couplings from A-twisted correlators
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• On Mirror Symmetry for Calabi-Yau Fourfolds with Three-Form Cohomology
• Givental J-functions, Quantum integrable systems, AGT relation with surface operator
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• tt* Geometry and a Twistorial Extension of Topological Strings
• Branes and 2d N=(2,2) gauge theories with orthogonal and symplectic groups
• 2D BPS Rings from Sphere Partition Functions
• Reconstructing GKZ via topological recursion
• Gravity Dual of Two-Dimensional $\mathcal{N}=(2,2{)}^{\ast }$ Supersymmetric Yang-Mills Theory and Integrable Models
• 2D Seiberg-like dualities with an adjoint matter
• Vortex counting and the quantum Hall effect
• Surface defects and instanton partition functions
• Exact Results for SYM on $Y^{p,q}$ and $S^2\times S^2$ with Conical Singularities
• On N=2 supersymmetric gauge theories on S^2XS^2
• Super-Weyl Anomaly from Holography and Rigid Supersymmetry Algebra on Two-Sphere
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models
• Resurgence in 2-dimensional Yang-Mills and a genus altering deformation
• Janus interface in two-dimensional supersymmetric gauge theories
• Determinantal Calabi-Yau varieties in Grassmannians and the Givental $I$-functions
• Supersymmetric Wilson loops in two dimensions and duality
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• 2d dualities from 4d
• Integrability As Duality: The Gauge/YBE Correspondence
• Four-Dimensional N=2 Supersymmetric Theory with Boundary as a Two-Dimensional Complex Toda Theory
• Cluster-Enriched Yang-Baxter Equation from SUSY Gauge Theories
• Correlation functions in massive Landau-Ginzburg orbifolds and tests of dualities
• Intersecting Surface defects and 3d Superconformal indices
• Nonabelian mirrors and Gromov-Witten invariants
• Mirror Symmetry and Partition Functions
• On Calabi-Yau manifolds in weighted projective spaces and their mirror GLSMs
• Localization of Gauged Linear Sigma Model for KK5-branes
• Spectral Sequences and Vacua in N = 2 Gauged Linear Quantum Mechanics with Potentials
• Wall-crossing for vortex partition function and handsaw quiver varierty
• Fixed points of (0,2) Landau-Ginzburg renormalization group flows and the chiral algebra
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• GLSM for Calabi-Yau Manifolds of Berglund-Hubsch Type
• Vortex-strings in N=2 quiver X U(1) theories
• Comments on Quantum Higgs Vacua
• Comments on supersymmetric renormalization in two-dimensional curved spacetime
• On supermatrix models, Poisson geometry and noncommutative supersymmetric gauge theories
• On gauged linear sigma models with torsion
• A Localization Computation in Confining Phase
• Exact Multi-Instanton Solutions to Selfdual Yang-Mills Equation on Curved Spaces
• On N=1 partition functions without R-symmetry
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Factorization of the 3d superconformal index with an adjoint matter
• 2D Seiberg-like dualities for orthogonal gauge groups
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$
• Supersymmetric Localization in GLSMs for Supermanifolds
• Localizing non-linear $\mathcal{N}=(2,2)$ sigma model on $S^2$
• N=(4,4) Vector Multiplets on Curved Two-Manifolds
• A survey of recent developments in GLSMs
• Gauge theories on spheres with 16 supercharges and non-constant couplings
• N=2 Chern-Simons-Matter Theories Without Vortices
• The braneology of 3D dualities
• Stringy Instanton Counting and Topological Strings
• Coincidences between Calabi-Yau manifolds of Berglund-Hubsch type and Batyrev polytopes
• Large $N$ limits of supersymmetric quantum field theories: A pedagogical overview
• A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture
• Kac-Moody Algebras on Soft Group Manifolds
• Schur Connections: Chord Counting, Line Operators, and Indices
• Partition functions for supersymmetric gauge theories on spheres