Supersymmetric partition functions and the three-dimensional A-twist

Abstract

We study three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories on ${\mathcal{M}}_{g,p}$, an oriented circle bundle of degree $p$ over a closed Riemann surface, ${\Sigma }_g$. We compute the ${\mathcal{M}}_{g,p}$ supersymmetric partition function and correlation functions of supersymmetric loop operators. This uncovers interesting relations between observables on manifolds of different topologies. In particular, the familiar supersymmetric partition function on the round $S^3$ can be understood as the expectation value of a so-called "fibering operator" on $S^2\times S^1$ with a topological twist. More generally, we show that the 3d $\mathcal{N}=2$ supersymmetric partition functions (and supersymmetric Wilson loop correlation functions) on ${\mathcal{M}}_{g,p}$ are fully determined by the two-dimensional A-twisted topological field theory obtained by compactifying the 3d theory on a circle. We give two complementary derivations of the result. We also discuss applications to F-maximization and to three-dimensional supersymmetric dualities.

arXiv comment84 pages plus appendix, 8 figures; v2: added references

References in corpus (52)

• Phases of $N=2$ Theories In Two Dimensions
• Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
• Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
• 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
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Notes on SUSY Gauge Theories on Three-Sphere
• Supersymmetric vacua and Bethe ansatz
• Summing the Instantons: Quantum Cohomology and Mirror Symmetry in Toric Varieties
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Elliptic genera of 2d N=2 gauge theories
• The complete superconformal index for N=6 Chern-Simons theory
• Exact Results in D=2 Supersymmetric Gauge Theories
• Seiberg Duality in Chern-Simons Theory
• On Mirror Symmetry in Three Dimensional Abelian Gauge Theories
• A topologically twisted index for three-dimensional supersymmetric theories
• Index for three dimensional superconformal field theories with general R-charge assignments
• Dilogarithm identities
• 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
• F-Theorem without Supersymmetry
• Comments on 3d Seiberg-like dualities
• Comments on Chern-Simons Contact Terms in Three Dimensions
• Supersymmetric Field Theories on Three-Manifolds
• Holomorphic Blocks in Three Dimensions
• The Geometry of Supersymmetric Partition Functions
• Aspects of Non-Abelian Gauge Dynamics in Two-Dimensional N=(2,2) Theories
• Supersymmetry on Curved Spaces and Holography
• Witten Index and Wall Crossing
• Comments on twisted indices in 3d supersymmetric gauge theories
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Derivation of the Verlinde Formula from Chern-Simons Theory and the G/G model
• Large $N$ matrix models for 3d $\mathcal{N}=2$ theories: twisted index, free energy and black holes
• The equivariant A-twist and gauged linear sigma models on the two-sphere
• Chern-Simons Theory on S^1-Bundles: Abelianisation and q-deformed Yang-Mills Theory
• Large $N$ topologically twisted index: necklace quivers, dualities, and Sasaki-Einstein spaces
• Bethe/Gauge correspondence on curved spaces
• Localization on Three-Manifolds
• Comments on N=(2,2) Supersymmetry on Two-Manifolds
• Factorisation and holomorphic blocks in 4d
• The large N limit of M2-branes on Lens spaces
• Exact results for supersymmetric abelian vortex loops in 2+1 dimensions
• F-theorem, duality and SUSY breaking in one-adjoint Chern-Simons-Matter theories
• On the reduction of 4d N=1 theories on S^2
• On Diagonalization in Map(M,G)
• Generalized Indices for $\mathcal{N}=1$ Theories in Four-Dimensions
• The long flow to freedom
• Chern-Simons Theory on Seifert 3-Manifolds
• A Crack in the Conformal Window
• Refined Checks and Exact Dualities in Three Dimensions

Cited by in corpus (67)

• $\mathcal{N}=1$ supersymmetric indices and the four-dimensional A-model
• An extremization principle for the entropy of rotating BPS black holes in AdS${}_5$
• A Universal Counting of Black Hole Microstates in AdS${}_4$
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• Holographic microstate counting for AdS${}_4$ black holes in massive IIA supergravity
• Topologically twisted indices in five dimensions and holography
• Microscopic Entropy of Rotating Electrically Charged AdS${}_4$ Black Holes from Field Theory Localization
• 5d Partition Functions with A Twist
• Localization of the action in AdS/CFT
• Sub-leading Structures in Superconformal Indices: Subdominant Saddles and Logarithmic Contributions
• A Bethe Ansatz type formula for the superconformal index
• Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
• Three-dimensional $\mathcal{N}=2$ supersymmetric gauge theories and partition functions on Seifert manifolds: A review
• Universal 3d Cardy Block and Black Hole Entropy
• Delayed Deconfinement and the Hawking-Page Transition
• Toward Microstate Counting Beyond Large N in Localization and the Dual One-loop Quantum Supergravity
• Large $N$ Partition Functions of the ABJM Theory
• Partition functions on 3d circle bundles and their gravity duals
• M-theoretic Genesis of Topological Phases
• Precision Microstate Counting for the Entropy of Wrapped M5-branes
• Black hole microstate counting in Type IIB from 5d SCFTs
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Supersymmetric Rényi entropy and charged hyperbolic black holes
• Factorization of log-corrections in AdS${}_4$/CFT${}_3$ from supergravity localization
• From 3d duality to 2d duality
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• 4d N=2 supergravity observables from Nekrasov-like partition functions
• 3d-3d correspondence for mapping tori
• Large $N$ twisted partition functions in 3d-3d correspondence and Holography
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Higher-Derivative Supergravity, Wrapped M5-branes, and Theories of Class $\mathcal{R}$
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Universal Logarithmic Behavior in Microstate Counting and the Dual One-loop Entropy of AdS${}_4$ Black Holes
• Microstates of rotating AdS${}_5$ strings
• Minimal $(D,D)$ conformal matter and generalizations of the van Diejen model
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Chiral 3d SU(3) SQCD and N=2 mirror duality
• Holonomy Saddles and Supersymmetry
• A-twisted correlators and Hori dualities
• Expanding 3d $\mathcal{N}=2$ Theories around the Round Sphere
• 3d $\mathcal{N}=2$ $\widehat{ADE}$ Chern-Simons Quivers
• Quantum Phases of $4d$ $SU(N)$ $\mathcal{N}=4$ SYM
• Topologically twisted index of $T[SU(N)]$ at large $N$
• Twisted indices, Bethe ideals and 3d $\mathcal{N}=2$ infrared dualities
• SYM on Quotients of Spheres and Complex Projective Spaces
• 3d defects in 5d: RG flows and defect F-maximization
• Infrared phases of 3D Class R theories
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Partition Functions and Fibering Operators on the Coulomb Branch of 5d SCFTs
• Exact WKB Analysis of ${\mathbb{CP}}^1$ Holomorphic Blocks
• Localization and Non-Renormalization in Chern-Simons Theory
• Generalized non-unitary Haagerup-Izumi modular data from 3D S-fold SCFTs
• On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels
• Mirror Symmetry and Mixed Chern-Simons Levels for Abelian 3d $\mathcal{N}=2$ theories
• Five-dimensional cohomological localization and squashed $q$-deformations of two-dimensional Yang-Mills theory
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Confinement and Graded Partition Functions for $\mathcal{N}=4$ SYM
• A Family of Vertex Algebras from Argyres-Douglas Theory
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Supersymmetry Breaking Phase in Three Dimensional Large N Gauge Theories
• Algebras, traces, and boundary correlators in $\mathcal{N}=4$ SYM
• Decomposition squared
• Magnetically charged AdS5 black holes from class S theories on hyperbolic 3-manifolds
• Three Dimensional Topological Field Theories and Nahm Sum Formulas
• 3D-3D Correspondence from Seifert Fibering Operators
• Stokes Phenomena in 3d $\mathcal{N}=2$ SQED${}_2$ and ${\mathbb{CP}}^1$ Models