Notes on SUSY Gauge Theories on Three-Sphere

Abstract

We extend the formula for partition functions of N=2 superconformal gauge theories on S^3 obtained recently by Kapustin, Willett and Yaakov, to incorporate matter fields with arbitrary R-charge assignments. We use the result to check that the self-mirror property of N=4 SQED with two electron hypermultiplets is preserved under a certain mass deformation which breaks the supersymmetry to N=2.

1+13 pages, (v3) one section added to present an integral formula for the partition function of general gauge theory. The version published in JHEP

References in corpus (15)

• Liouville Correlation Functions from Four-dimensional Gauge Theories
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• Mirror Symmetry in Three Dimensional Gauge Theories
• A_{N-1} conformal Toda field theory correlation functions from conformal N=2 SU(N) quiver gauge theories
• Counting chiral primaries in N=1 d=4 superconformal field theories
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• 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
• 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
• Dynamics of N=2 Supersymmetric Chern-Simons Theories
• On Large N Solution of ABJM Theory
• Large N duality beyond the genus expansion

Cited by in corpus (310)

• Towards the F-Theorem: N=2 Field Theories on the Three-Sphere
• The Exact Superconformal R-Symmetry Extremizes Z
• Rigid Supersymmetric Theories in Curved Superspace
• SUSY Gauge Theories on Squashed Three-Spheres
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• ABJM theory as a Fermi gas
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Comments on 3d Seiberg-like dualities
• Supersymmetric Field Theories on Three-Manifolds
• Bootstrapping the superconformal index with surface defects
• 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
• The Geometry of Supersymmetric Partition Functions
• N=2 supersymmetric theories on squashed three-sphere
• Supersymmetry on Curved Spaces and Holography
• Exploring Curved Superspace
• Supersymmetric Gauge Theories on the Five-Sphere
• Instanton Effects in ABJM Theory from Fermi Gas Approach
• SL(2,R) Chern-Simons, Liouville, and Gauge Theory on Duality Walls
• The $\mathcal{N}=8$ Superconformal Bootstrap in Three Dimensions
• The string origin of dyonic $\mathcal{N}=8$ supergravity and its simple Chern-Simons duals
• Correlation Functions of Coulomb Branch Operators
• 4d Index to 3d Index and 2d TQFT
• From 4d superconformal indices to 3d partition functions
• 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
• Instanton Bound States in ABJM Theory
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• On Three Dimensional Quiver Gauge Theories and Integrability
• Membrane instantons from a semiclassical TBA
• 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
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• Supersymmetric Wilson loops in N=4 super Chern-Simons-matter theory
• 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
• Explicit examples of DIM constraints for network matrix models
• The large N limit of quiver matrix models and Sasaki-Einstein manifolds
• Deformation quantization and superconformal symmetry in three dimensions
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Perturbative partition function for a squashed S^5
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Holography for $\mathcal{N}=2^{\ast }$ on $S^4$
• Calculating the partition function of N=2 Gauge theories on $S^3$ and AdS/CFT correspondence
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Exact Results in Supersymmetric Field Theories on Manifolds with Boundaries
• SUSY monopole potentials in 2+1 dimensions
• Black hole entropy in massive Type IIA
• 3d Chern-Simons Theory from M5-branes
• From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
• 3d & 5d gauge theory partition functions as q-deformed CFT correlators
• Localization in Supergravity and Quantum $Ad{S}_4/CF{T}_3$ Holography
• Probing non-perturbative effects in M-theory
• Exact results on ABJ theory and the refined topological string
• Coulomb Branch Operators and Mirror Symmetry in Three Dimensions
• Localization on Three-Manifolds
• Matrix models from operators and topological strings
• 3D-partition functions on the sphere: exact evaluation and mirror symmetry
• Three-sphere free energy for classical gauge groups
• Extended Supersymmetry on Curved Spaces
• Direct derivation of "mirror" ABJ partition function
• The Omega Deformation From String and M-Theory
• ABJ Fractional Brane from ABJM Wilson Loop
• The large N limit of M2-branes on Lens spaces
• Exploring Curved Superspace (II)
• From Rigid Supersymmetry to Twisted Holomorphic Theories
• Instanton effects in ABJM theory with general R-charge assignments
• M-theoretic matrix models
• ABJM Wilson Loops in Arbitrary Representations
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• Rank $Q$ E-string on a torus with flux
• Localization of 3d $\mathcal{N}=2$ Supersymmetric Theories on $S^1\times D^2$
• Argyres-Douglas Theories, S^1 Reductions, and Topological Symmetries
• Aharony Dualities for 3d Theories with Adjoint Matter
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Localization on three-dimensional manifolds
• S^3/Z_n partition function and dualities
• S-duality and the N=2 Lens Space Index
• Partition Functions of Superconformal Chern-Simons Theories from Fermi Gas Approach
• Quivers, YBE and 3-manifolds
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Boundary Terms and Three-Point Functions: An AdS/CFT Puzzle Resolved
• Universal 3d Cardy Block and Black Hole Entropy
• N=2 Dualities and Z Extremization in Three Dimensions
• On RG Flow of tau_{RR} for Supersymmetric Field Theories in Three-Dimensions
• N=2 S-duality Revisited
• Supersymmetry on Three-dimensional Lorentzian Curved Spaces and Black Hole Holography
• 5D SYM and 2D q-Deformed YM
• N=2 supersymmetric AdS_4 solutions of M-theory
• High-Temperature Expansion of Supersymmetric Partition Functions
• Accidental Symmetries and the Conformal Bootstrap
• Three-Dimensional Superconformal Field Theory on Conic Space as Hologram of Charged Topological Black Hole
• Matrix Models for Supersymmetric Chern-Simons Theories with an ADE Classification
• 5D SYM on 3D Sphere and 2D YM
• Comments on the Casimir energy in supersymmetric field theories
• Symmetry enhancement and closing of knots in 3d/3d correspondence
• 3d N=2 mirror symmetry, pq-webs and monopole superpotentials
• Dualities for 3d Theories with Tensor Matter
• Supersymmetric Rényi Entropy in Five Dimensions
• Superconformal indices of $\mathcal{N}=4$ SYM field theories
• Aspects of Defects in 3d-3d Correspondence
• Refined test of AdS4/CFT3 correspondence for N=2,3 theories
• D2-brane Chern-Simons theories: F-maximization = a-maximization
• Instanton Effects in Orbifold ABJM Theory
• On Supersymmetric Gauge Theories on S^4 x S^1
• $USp(2N_c)$ SQCD${}_3$ with antisymmetric: dualities and symmetry enhancements
• The gravity dual of supersymmetric gauge theories on a squashed $S^1\times S^3$
• The F-Theorem and F-Maximization
• From 3d dualities to 2d free field correlators and back
• Seiberg dualities and the 3d/4d connection
• N = 4 Super-Yang-Mills on Conic Space as Hologram of STU Topological Black Hole
• The Large N Limit of Toric Chern-Simons Matter Theories and Their Duals
• The ABCDEF's of Matrix Models for Supersymmetric Chern-Simons Theories
• Interacting fermions and N=2 Chern-Simons-matter theories
• Partition functions on 3d circle bundles and their gravity duals
• Spectral zeta function and non-perturbative effects in ABJM Fermi-gas
• Supersymmetric Localization for BPS Black Hole Entropy: 1-loop Partition Function from Vector Multiplets
• Cardy Formula for 4d SUSY Theories and Localization
• Operator Counting and Eigenvalue Distributions for 3D Supersymmetric Gauge Theories
• On matrix models and their $q$-deformations
• A slow review of the AGT correspondence
• Coulomb Branch Quantization and Abelianized Monopole Bubbling
• ABJM on ellipsoid and topological strings
• Intersecting Surface Defects and Instanton Partition Functions
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• 3d $\mathcal{N}=4$ OPE Coefficients from Fermi Gas
• Global Supersymmetry on Curved Spaces in Various Dimensions
• Superconformal Index with Duality Domain Wall
• Dualities and Phases of 3D N=1 SQCD
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Rigid 6D supersymmetry and localization
• Supersymmetry of the C-metric and the general Plebanski-Demianski solution
• A Crack in the Conformal Window
• 3d dualities from 2d free field correlators: recombination and rank stabilization
• Quantum Phase Transitions in Mass-Deformed ABJM Matrix Model
• From S-confinement to 3D Chiral Theories: Dressing the Monopoles
• Black holes with baryonic charge and $\mathcal{I}$-extremization
• Exact relations between M2-brane theories with and without Orientifolds
• Vanishing superconformal indices and the chiral symmetry breaking
• Exact Instanton Expansion of ABJM Partition Function
• 4d $S$-duality wall and $SL(2,\mathbb{Z})$ relations
• Supersymmetric $U(N)$ Chern-Simons-matter theory and phase transitions
• A 5d/3d duality from relativistic integrable system
• Eigenvalue Distributions in Matrix Models for Chern-Simons-matter Theories
• Large N behavior of mass deformed ABJM theory
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• Localization at large N in Chern-Simons-matter theories
• Free Energy of D_n Quiver Chern-Simons Theories
• An introduction to supersymmetric field theories in curved space
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Toric Fano varieties and Chern-Simons quivers
• Chern-Simons and RG Flows: Contact with Dualities
• 5d Higgs Branch Localization, Seiberg-Witten Equations and Contact Geometry
• Localization of Supersymmetric Chern-Simons-Matter Theory on a Squashed $S^3$ with $SU(2)\times U(1)$ Isometry
• Romans-mass-driven flows on the D2-brane
• Free Energy vs Sasaki-Einstein Volume for Infinite Families of M2-Brane Theories
• T-branes, monopoles and S-duality
• Refined Checks and Exact Dualities in Three Dimensions
• Magnetic quivers and line defects -- On a duality between 3d N=4 unitary and orthosymplectic quivers
• The free energy of N=2 supersymmetric AdS_4 solutions of M-theory
• BPS Wilson loops in $\mathcal{N}\ge 2$ superconformal Chern-Simons-matter theories
• $\mathcal{N}=2$ supersymmetric field theories on 3-manifolds with A-type boundaries
• Perturbative c-theorem in d-dimensions
• Mirror theories of 3d $\mathcal{N}=2$ SQCD
• Ellipsoid partition function from Seiberg-Witten monopoles
• N=2 SUSY gauge theories on S^4
• Dualities for three-dimensional $\mathcal{N}=2$ $SU(N_c)$ chiral adjoint SQCD
• Supersymmetric backgrounds from 5d N=1 supergravity
• Z-extremization and F-theorem in Chern-Simons matter theories
• Supersymmetry and Mass Gap in 2+1 Dimensions: A Gauge Invariant Hamiltonian Analysis
• Supersymmetric solutions and Borel singularities for N=2 supersymmetric Chern-Simons theories
• On 3d Seiberg-like Dualities with Two Adjoints
• Topological anomalies for Seifert 3-manifolds
• New 3d $\mathcal{N}=2$ SCFT's with $N^{3/2}$ scaling
• The $SL(2,\mathbb{Z})$ dualization algorithm at work
• Notes on hyperloops in N=4 Chern-Simons-matter theories
• Complete factorization in minimal N=4 Chern-Simons-matter theory
• Wrapped Brane Solutions in Romans $F(4)$ Gauged Supergravity
• Wilson loops and the geometry of matrix models in AdS_4/CFT_3
• Extended global symmetries for 4d N=1 SQCD theories
• Mass Deformed ABJM Theory on Three Sphere in Large N limit
• Comments on knotted 1/2 BPS Wilson loops
• BPS Wilson loops and quiver varieties
• Superfield theories on $S^3$ and their localization
• Mirror Symmetry in Three Dimensions via Gauged Linear Quivers
• Picard-Lefschetz decomposition and Cheshire Cat resurgence in 3D $\mathcal{N}=2$ field theories
• Interpolating Wilson loops and enriched RG flows
• Localization on round sphere revisited
• Refined 3d-3d Correspondence
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Flowing to $\mathcal{N}=3$ Chern--Simons-matter theory
• ABJ Correlators with Weakly Broken Higher Spin Symmetry
• 4d partition function on S^1 x S^3 and 2d Yang-Mills with nonzero area
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• N=4 supersymmetric Yang-Mills theories in AdS_3
• ABJ Quadrality
• Line operators in Chern-Simons-Matter theories and Bosonization in Three Dimensions II -Perturbative Analysis and All-loop Resummation
• Universal Features of Four-Dimensional Superconformal Field Theory on Conic Space
• Comments on F-maximization and R-symmetry in 3D SCFTs
• On Large N Solution of N=3 Chern-Simons-adjoint Theories
• Z Extremization in Chiral-Like Chern Simons Theories
• 3d Deconfinement, Product gauge group, Seiberg-Witten and New 3d dualities
• Duality and Transport for Supersymmetric Graphene from the Hemisphere Partition Function
• Taming Supersymmetric Defects in 3d-3d Correspondence
• Notes on Integral Identities for 3d Supersymmetric Dualities
• String theory and the 4D/3D reduction of Seiberg duality. A Review
• 3d N=4 Bootstrap and Mirror Symmetry
• On dimensional reduction of 4d N=1 Lagrangians for Argyres-Douglas theories
• One-Dimensional Sectors From the Squashed Three-Sphere
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Large-N reduction for N=2 quiver Chern-Simons theories on S^3 and localization in matrix models
• Generalized Giveon-Kutasov duality
• Connecting Mirror Symmetry in 3d and 2d via Localization
• The topological line of ABJ(M) theory
• A Note On 3D N=2 Dualities: Real Mass Flow And Partition Function
• SYM on Quotients of Spheres and Complex Projective Spaces
• Challenges of beta-deformation
• New 3d $\mathcal{N}=2$ Dualities from Quadratic Monopoles
• 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 $N_f=1$
• 3d defects in 5d: RG flows and defect F-maximization
• Localization and Large N reduction on S^3 for the Planar and M-theory limit
• Exact results for ABJ Wilson loops and open-closed duality
• Localization principle in SUSY gauge theories
• Wilson loops and defect RG flows in ABJM
• On the exact R charge for N=2 CS theories
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Quantum phase transition and Resurgence: Lessons from 3d $\mathcal{N}=4$ SQED
• Resurgence and Lefschetz thimble in 3d N=2 supersymmetric Chern-Simons matter theories
• Supersymmetry Breaking in a Large N Gauge Theory with Gravity Dual
• Exact SUSY Wilson loops on $S^3$ from $q$-Virasoro constraints
• Web of Seiberg-like dualities for 3d $\mathcal{N}=2$ quivers
• Partition Function of $N=2$ Gauge Theories on a Squashed $S^4$ with $SU(2)\times U(1)$ Isometry
• Super-Yang-Mills theories on S4 x R
• $QC{D}_3$ Dualities and the F-Theorem
• Non-perturbative Tests of Duality Cascades in Three Dimensional Supersymmetric Gauge Theories
• Branes, partition functions and quadratic monopole superpotentials
• Superconformal structures on the three-sphere
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• 5D SYM on 3D Deformed Spheres
• Conformal and non-conformal hyperloop deformations of the 1/2 BPS circle
• Gauging and Decoupling in 3d $\mathcal{N}=2$ dualities
• Localization and Non-Renormalization in Chern-Simons Theory
• Solving Mass-deformed Holography Perturbatively
• Exact solution of Chern-Simons-matter matrix models with characteristic/orthogonal polynomials
• Identification of Bulk coupling constant in Higher Spin/ABJ correspondence
• The $\mathcal{N}=2$ Prepotential and the Sphere Free Energy
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• Classifying BPS bosonic Wilson loops in 3d $\mathcal{N}=4$ Chern-Simons-matter theories
• Operator Counting for N=2 Chern-Simons Gauge Theories with Chiral-like Matter Fields
• Dualities for adjoint SQCD in three dimensions and emergent symmetries
• Recent developments in 2d $\mathcal{N}=(2,2)$ supersymmetric gauge theories
• A perturbative study of holographic mABJM theory
• S-duality wall of SQCD from Toda braiding
• Ramond-Ramond couplings of D-branes
• 3d $\mathcal{N}=3$ Generalized Giveon-Kutasov Duality
• Mordell integrals and Giveon-Kutasov duality
• Webs of 3d $\mathcal{N}=2$ dualities with D-type superpotentials
• 3D ${\tau }_{RR}$-minimization in AdS${}_4$ gauged supergravity
• Pentagon identities arising in supersymmetric gauge theory computations
• Higgs and Coulomb Branch Descriptions of the Volume of the Vortex Moduli Space
• Deconstructing Defects
• Curvature Couplings in $\mathcal{N}=(2,2)$ Nonlinear Sigma Models on $S^2$
• Chiral dualities for SQCD${}_3$ with D-type superpotential
• Gravitating anisotropic merons and squashed spheres in the three-dimensional Einstein-Yang-Mills-Chern-Simons theory
• Spin(7) duality for N=1 CS-matter theories
• Exact results for Wilson loops in orbifold ABJM theory
• Supersymmetric gauge theory on curved 7-branes
• Mass deformed ABJM and $\mathcal{P}\mathcal{T}$ symmetry
• Subleading corrections to the free energy in a theory with $N^{5/3}$ scaling
• BPS Wilson loops in mass-deformed ABJM theory: Fermi gas expansions and new defect CFT data
• Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit
• BPS states and their reductions
• Exact large $N$ expansion of $\mathcal{N}=4$ circular quiver Chern-Simons theories and squashing
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• Klebanov-Witten flows in M-theory
• Intersecting Surface defects and 3d Superconformal indices
• 3d dualities with decoupled sectors and brane transitions
• 4d/3d reduction of s-confining theories: the role of the "exotic" D instantons
• On ${\mathrm{SQED}}_3$ and ${\mathrm{SQCD}}_3$: phase transitions and integrability
• Matrix Model of Chern-Simons Matter Theories Beyond The Spherical Limit
• Supersymmetry Breaking Phase in Three Dimensional Large N Gauge Theories
• Holographic supersymmetric Renyi entropies from hyperbolic black holes with scalar hair
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• Dualities and loops on squashed $S^3$
• BPS $M2$-branes in $Ad{S}_4\times Q^{1,1,1}$ Dual to Loop Operators
• Toward the construction of the general multi-cut solutions in Chern-Simons Matrix Models
• Localization of Gauged Linear Sigma Model for KK5-branes
• $S^1$ Reduction of 4D $\mathcal{N}=3$ SCFTs and Squashing Independence of ABJM Theories
• Large-$N$ Free Energy of Chiral $\mathcal{N}=2$ Chern-Simons-Matter Theories
• Supersymmetric localization: $\mathcal{N}=(2,2)$ theories on S${}^2$ and AdS${}_2$
• Supersymmetric localisation of $\mathcal{N}=(2,2)$ theories on a spindle
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models
• N=2 Chern-Simons-Matter Theories Without Vortices
• Symmetry breaking caused by large R-charge
• Holographic Wilson Loop One-point Functions in ABJM Theory
• A network of hyperloops
• QFT Realization of Non-Unitary $\mathfrak{sl}(2,\mathbb{C})$ WRT Invariants and Their Galois Conjugations
• Matrix models from localization of five-dimensional supersymmetric noncommutative U(1) gauge theory
• A Nonperturbative Proof of Dijkgraaf-Vafa Conjecture
• Single-flavor Abelian mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$