SUSY Gauge Theories on Squashed Three-Spheres

Abstract

We study Euclidean 3D N=2 supersymmetric gauge theories on squashed three-spheres preserving isometries SU(2) x U(1) or U(1) x U(1). We show that, when a suitable background U(1) gauge field is turned on, these squashed spheres support charged Killing spinors and therefore N=2 supersymmetric gauge theories. We present the Lagrangian and supersymmetry rules for general gauge theories. The partition functions are computed using localization principle, and are expressed as integrals over Coulomb branch. For the squashed sphere with U(1) x U(1) isometry, its measure and integrand are identified with the building blocks of structure constants in Liouville or Toda conformal field theories with b \neq 1.

1+21 pages, no figure

References in corpus (18)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Notes on SUSY Gauge Theories on Three-Sphere
• The complete superconformal index for N=6 Chern-Simons theory
• Index for three dimensional superconformal field theories with general R-charge assignments
• The Omega Deformation, Branes, Integrability, and Liouville Theory
• Nonperturbative Tests of Three-Dimensional Dualities
• Exact Results in ABJM Theory from Topological Strings
• A supermatrix model for N=6 super Chern-Simons-matter theory
• The Virtue of Defects in 4D Gauge Theories and 2D CFTs
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Unitary representations of $U_{q}(\mathfrak{sl}(2,\RR))$, the modular double, and the multiparticle q-deformed Toda chains
• AGT on the S-duality Wall
• Exact Results and Holography of Wilson Loops in N=2 Superconformal (Quiver) Gauge Theories
• Refined test of AdS4/CFT3 correspondence for N=2,3 theories
• On Large N Solution of ABJM Theory
• Large N duality beyond the genus expansion

Cited by in corpus (337)

• Rigid Supersymmetric Theories in Curved Superspace
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• 3d dualities from 4d dualities
• A topologically twisted index for three-dimensional supersymmetric theories
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• 5-dim Superconformal Index with Enhanced En Global Symmetry
• Comments on 3d Seiberg-like dualities
• Supersymmetric Field Theories on Three-Manifolds
• Holomorphic Blocks in Three Dimensions
• The perturbative partition function of supersymmetric 5D Yang-Mills theory with matter on the five-sphere
• Summing Up All Genus Free Energy of ABJM Matrix Model
• M-Strings
• The Geometry of Supersymmetric Partition Functions
• N=2 supersymmetric theories on squashed three-sphere
• Exact results for the entanglement entropy and the energy radiated by a quark
• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Supersymmetric Gauge Theories on the Five-Sphere
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• Factorisation of N = 2 theories on the squashed 3-sphere
• Defects and Quantum Seiberg-Witten Geometry
• Seiberg-Witten Theories on Ellipsoids
• Exact Kahler Potential from Gauge Theory and Mirror Symmetry
• Numerical studies of the ABJM theory for arbitrary N at arbitrary coupling constant
• The gravity dual of supersymmetric gauge theories on a squashed three-sphere
• The Holography of F-maximization
• On Three Dimensional Quiver Gauge Theories and Integrability
• Relation between the 4d superconformal index and the S^3 partition function
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Higgs branch localization in three dimensions
• Dual Boundary Conditions in 3d SCFT's
• Supersymmetric partition functions and the three-dimensional A-twist
• The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
• Supersymmetric Renyi Entropy
• Deformation quantization and superconformal symmetry in three dimensions
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• Perturbative partition function for a squashed S^5
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Braids, Walls, and Mirrors
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• Supersymmetry in Lorentzian Curved Spaces and Holography
• EFT and the SUSY Index on the 2nd Sheet
• SUSY monopole potentials in 2+1 dimensions
• BPS Wilson loops and Bremsstrahlung function in ABJ(M): a two loop analysis
• An E7 Surprise
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Higgs branch localization of 3d N=2 theories
• Localization on Three-Manifolds
• The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• Extended Supersymmetry on Curved Spaces
• 5d Partition Functions with A Twist
• Carving Out the End of the World or (Superconformal Bootstrap in Six Dimensions)
• The Omega Deformation From String and M-Theory
• High-temperature asymptotics of supersymmetric partition functions
• The supersymmetric NUTs and bolts of holography
• The large N limit of M2-branes on Lens spaces
• 3-Manifolds and 3d Indices
• Reducing the 4d Index to the S^3 Partition Function
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• The supersymmetric index in four dimensions
• Superconformal Partition Functions and Non-perturbative Topological Strings
• Holographic duals of 3d S-fold CFTs
• 3d analogs of Argyres-Douglas theories and knot homologies
• Rank $Q$ E-string on a torus with flux
• tt* Geometry in 3 and 4 Dimensions
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• Supersymmetry on curved spaces and superconformal anomalies
• The Partition Function of ABJ Theory
• AdS${}_4$/CFT${}_3$ from Weak to Strong String Coupling
• Decoding a Three-Dimensional Conformal Manifold
• Seiberg-like Dualities for 3d N=2 Theories with SU(N) gauge group
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• S^3/Z_n partition function and dualities
• Flipping the head of T[SU(N)]: mirror symmetry, spectral duality and monopoles
• Localization on three-dimensional manifolds
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Quivers, YBE and 3-manifolds
• Universality of squashed-sphere partition functions
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Universal 3d Cardy Block and Black Hole Entropy
• Supersymmetric theories on squashed five-sphere
• Rotating Black Hole Entropy from M5-branes
• N=2 Dualities and Z Extremization in Three Dimensions
• High-Temperature Expansion of Supersymmetric Partition Functions
• Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography
• Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole
• Gauge/Liouville Triality
• Rigid Supersymmetric Backgrounds of Minimal Off-Shell Supergravity
• Redeeming Bad Theories
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• The gravity dual of supersymmetric gauge theories on a two-parameter deformed three-sphere
• Supersymmetric Boundary Conditions in Three Dimensional N = 2 Theories
• Supersymmetric Rényi Entropy in Five Dimensions
• Aspects of Defects in 3d-3d Correspondence
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• The Gravity Dual of Supersymmetric Renyi Entropy
• Super-Rényi Entropy & Wilson Loops for N=4 SYM and their Gravity Duals
• On Supersymmetric Gauge Theories on S^4 x S^1
• The gravity dual of supersymmetric gauge theories on a squashed five-sphere
• Seiberg dualities and the 3d/4d connection
• From 3d dualities to 2d free field correlators and back
• The superconformal index and an elliptic algebra of surface defects
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• The holographic supersymmetric Renyi entropy in five dimensions
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• On 3d extensions of AGT relation
• Emergent 3-manifolds from 4d Superconformal Indices
• Partition functions on 3d circle bundles and their gravity duals
• Cardy Formula for 4d SUSY Theories and Localization
• Schur correlation functions on $S^3\times S^1$
• Gauge Theories Labelled by Three-Manifolds
• On matrix models and their $q$-deformations
• A slow review of the AGT correspondence
• Factorization of S^3/Z_n partition function
• Spherical Branes
• N=2 gauge theories on the hemisphere $H{S}^4$
• ABJM on ellipsoid and topological strings
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• Intersecting Surface Defects and Instanton Partition Functions
• Global Supersymmetry on Curved Spaces in Various Dimensions
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• The star-triangle relation and 3d superconformal indices
• ABJM at Strong Coupling from M-theory, Localization, and Lorentzian Inversion
• Wilson loops in supersymmetric Chern-Simons-matter theories and duality
• Squashing, Mass, and Holography for 3d Sphere Free Energy
• Holography of 3d-3d correspondence at Large N
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Comments on Squashed-sphere Partition Functions
• Boundaries, Vermas, and Factorisation
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Supersymmetry of the C-metric and the general Plebanski-Demianski solution
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• The NUTs and Bolts of Squashed Holography
• 3d-3d Correspondence Revisited
• Holomorphic Blocks for 3d Non-abelian Partition Functions
• Vanishing superconformal indices and the chiral symmetry breaking
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• ABJM at finite $N$ via 4d supergravity
• A 5d/3d duality from relativistic integrable system
• Deformed supersymmetric gauge theories from the fluxtrap background
• Supersymmetric Gauge Theories on a Squashed Four-Sphere
• Supersymmetric localization in two dimensions
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• Central charges from the $\mathcal{N}=1$ superconformal index
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Sphere correlation functions and Verma modules
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Introduction to localization in quantum field theory
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• 4d Quantum Geometry from 3d Supersymmetric Gauge Theory and Holomorphic Block
• An introduction to supersymmetric field theories in curved space
• $q$-Virasoro modular double and 3d partition functions
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Complex Chern-Simons from M5-branes on the Squashed Three-Sphere
• Chern-Simons and RG Flows: Contact with Dualities
• Two-Sphere Partition Functions and Gromov-Witten Invariants
• The 3d $\mathcal{N}=6$ Bootstrap: From Higher Spins to Strings to Membranes
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Smallest 3d hyperbolic manifolds via simple 3d theories
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Factorization of 4d N=1 superconformal index
• Exact relativistic Toda chain eigenfunctions from Separation of Variables and gauge theory
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• Partition functions on slightly squashed spheres and flux parameters
• T-branes, monopoles and S-duality
• Holography of Wrapped M5-branes and Chern-Simons theory
• Refined Checks and Exact Dualities in Three Dimensions
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Localization of supersymmetric field theories on non-compact hyperbolic three-manifolds
• Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
• A 3d-3d appetizer
• Monopole Quivers and new 3D N=2 dualities
• Mirror theories of 3d $\mathcal{N}=2$ SQCD
• Ellipsoid partition function from Seiberg-Witten monopoles
• N=2 SUSY gauge theories on S^4
• Supersymmetric D3/D5 for massive defects on curved space
• Supersymmetric backgrounds from 5d N=1 supergravity
• S-duality resurgence in SL(2) Chern-Simons theory
• 3d Mirror Symmetry from S-duality
• Supersymmetric Rényi Entropy in Two Dimensions
• Dualities for three-dimensional $\mathcal{N}=2$ $SU(N_c)$ chiral adjoint SQCD
• On Three-Dimensional Quiver Gauge Theories of Type B
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• Review of localization for 5d supersymmetric gauge theories
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Exact results for vortex loop operators in 3d supersymmetric theories
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Topological anomalies for Seifert 3-manifolds
• Vortices and 3 dimensional dualities
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• Extended global symmetries for 4d N=1 SQCD theories
• Localization on round sphere revisited
• BPS Wilson loops and quiver varieties
• Comments on knotted 1/2 BPS Wilson loops
• A matrix model for the latitude Wilson loop in ABJM theory
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Squashing and supersymmetry enhancement in three dimensions
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• Refined 3d-3d Correspondence
• A review on SUSY gauge theories on $S^3$
• Supersymmetric Rényi Entropy and Defect Operators
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• Entanglement Entropy of ABJM Theory and Entropy of Topological Black Hole
• Bethe/Gauge correspondence in odd dimension: modular double, non-perturbative corrections and open topological strings
• Star shaped quivers with flux
• Universal Features of Four-Dimensional Superconformal Field Theory on Conic Space
• 3d $\mathcal{N}=2$ minimal SCFTs from Wrapped M5-branes
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• 3d N=4 Bootstrap and Mirror Symmetry
• Gravity duals of supersymmetric gauge theories on three-manifolds
• One-Dimensional Sectors From the Squashed Three-Sphere
• String theory and the 4D/3D reduction of Seiberg duality. A Review
• Notes on Integral Identities for 3d Supersymmetric Dualities
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Supersymmetric localization of refined chiral multiplets on topologically twisted $H^2\times S^1$
• Connecting Mirror Symmetry in 3d and 2d via Localization
• Integrable lattice spin models from supersymmetric dualities
• Challenges of beta-deformation
• Localization and Duality for ABJM Latitude Wilson Loops
• Black hole microstates and supersymmetric localization
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• A Note On 3D N=2 Dualities: Real Mass Flow And Partition Function
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• SYM on Quotients of Spheres and Complex Projective Spaces
• Maximal super Yang-Mills theories on curved background with off-shell supercharges
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$
• Localization and Large N reduction on S^3 for the Planar and M-theory limit
• Supersymmetric vortex loops in 3D gauge theories
• Elliptic modular double and 4d partition functions
• 6j symbols for the modular double, quantum hyperbolic geometry, and supersymmetric gauge theories
• Bootstrapping the $S^5$ partition function
• Localization principle in SUSY gauge theories
• Adjoint Reidemeister torsions from wrapped M5-branes
• Infrared phases of 3D Class R theories
• Killing-Yano tensor and supersymmetry of the self-dual Plebanski-Demianski solution
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Gromov-Witten invariants and localization
• The ABCDEFG of Little Strings
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Branes, partition functions and quadratic monopole superpotentials
• Integral identities for 3d dualities with SP(2N) gauge groups
• Towards U(N|M) knot invariant from ABJM theory
• 5D SYM on 3D Deformed Spheres
• Super Yang-Mills on Branched Covers and Weighted Projective Spaces
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• ABJ Theory in the Higher Spin Limit
• Localization and Non-Renormalization in Chern-Simons Theory
• Dualities for adjoint SQCD in three dimensions and emergent symmetries
• Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• Complex Chern-Simons theory at level k via the 3d-3d correspondence
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• Ramond-Ramond couplings of D-branes
• Lens partition function, pentagon identity and star-triangle relation
• Entanglement in Theory Space
• Spectral sum rules for confining large-N theories
• Multiple sine, multiple elliptic gamma functions and rational cones
• Improvement of a conserved current density versus adding a total derivative to a Lagrangian density
• S-duality wall of SQCD from Toda braiding
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• General modular quantum dilogarithm and beta integrals
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Deconstructing Defects
• Webs of 3d $\mathcal{N}=2$ dualities with D-type superpotentials
• Pentagon identities arising in supersymmetric gauge theory computations
• Tangles, Generalized Reidemeister Moves, and Three-Dimensional Mirror Symmetry
• Euclidean supersymmetric solutions with the self-dual Weyl tensor
• Chiral dualities for SQCD${}_3$ with D-type superpotential
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• Surface defects and instanton partition functions
• Resummations and Non-Perturbative Corrections
• Cluster transformations, the tetrahedron equation and three-dimensional gauge theories
• Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory
• Holographic RG flows on Squashed $S^3$
• Higher-Curvature Gravity, Black Holes and Holography
• Higher-Derivative Supergravity, AdS${}_4$ Holography, and Black Holes
• Seven-dimensional super Yang-Mills at negative coupling
• BPS states and their reductions
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Supersymmetry Breaking Phase in Three Dimensional Large N Gauge Theories
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Bridging 4D QFTs and 2D VOAs via 3D high-temperature EFTs
• Constant maps in equivariant topological strings and geometric modeling of fluxes
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• 4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
• Intersecting Surface defects and 3d Superconformal indices
• Supersymmetric Graphene on Squashed Hemisphere
• A String Dual for Partially Topological Chern-Simons-Matter Theories
• A journey to 3d: exact relations for adjoint SQCD from dimensional reduction
• Holographic Duality for three-dimensional Super-conformal Field Theories
• On ${\mathrm{SQED}}_3$ and ${\mathrm{SQCD}}_3$: phase transitions and integrability
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Steady Euler flows and the Faddeev-Skyrme model with mass term
• A Localization Computation in Confining Phase
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• Dualities and loops on squashed $S^3$
• Mirror Symmetry And Loop Operators
• On the planar limit of 3d $T_{\rho }^{\sigma }[SU(N)]$
• Bootstrap of the defect 1/2 BPS Wilson lines in N=4 Chern-Simons-matter theories
• N=2 Chern-Simons-Matter Theories Without Vortices
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Defect Networks and Supersymmetric Loop Operators
• Topological phase, spin Chern-Simons theory and level rank duality on lens space
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$
• Quantum Trilogy: Discrete Toda, Y-System and Chaos
• Localization of four-dimensional super Yang-Mills theories compactified on Riemann surface
• QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
• Wrapped $M5$-branes and complex saddle points
• A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture
• Notes on holonomy matrices of hyperbolic 3-manifolds with cusps
• N=1 Chern-Simons-matter theory and localization
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
• A network of hyperloops
• Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories
• Kac-Moody Algebras on Soft Group Manifolds