Supersymmetric partition functions on Riemann surfaces

Abstract

We present a compact formula for the supersymmetric partition function of 2d N=(2,2), 3d N=2 and 4d N=1 gauge theories on ${\Sigma }_g\times T^n$ with partial topological twist on ${\Sigma }_g$, where ${\Sigma }_g$ is a Riemann surface of arbitrary genus and $T^n$ is a torus with n=0,1,2, respectively. In 2d we also include certain local operator insertions, and in 3d we include Wilson line operator insertions along $S^1$. For genus g=1, the formula computes the Witten index. We present a few simple Abelian and non-Abelian examples, including new tests of non-perturbative dualities. We also show that the large N partition function of ABJM theory on ${\Sigma }_g\times S^1$ reproduces the Bekenstein-Hawking entropy of BPS black holes in AdS${}_4$ whose horizon has ${\Sigma }_g$ topology.

34 pages, 1 figure

References in corpus (27)

• Electric-Magnetic Duality in Supersymmetric Non-Abelian Gauge Theories
• Phases of $N=2$ Theories In Two Dimensions
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Black hole microstates in AdS${}_4$ from supersymmetric localization
• Elliptic genera of 2d N=2 gauge theories
• Seiberg Duality in Chern-Simons Theory
• Elliptic genera of two-dimensional N=2 gauge theories with rank-one gauge groups
• IR Duality in d=3 N=2 Supersymmetric USp(2N_c) and U(N_c) Gauge Theories
• Comments on 3d Seiberg-like dualities
• Supersymmetric AdS_4 black holes and attractors
• Comments on twisted indices in 3d supersymmetric gauge theories
• Aspects of 3d N=2 Chern-Simons-Matter Theories
• Static supersymmetric black holes in AdS_4 with spherical symmetry
• Higgs branch localization in three dimensions
• Towards the Mirror Symmetry for Calabi-Yau Complete intersections in Gorenstein Toric Fano Varieties
• Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds
• M2-brane surface operators and gauge theory dualities in Toda
• Non-Abelian Localization for Supersymmetric Yang-Mills-Chern-Simons Theories on Seifert Manifold
• Log canonical singularities and complete moduli of stable pairs
• A Duality Appetizer
• G/G gauged WZW model and Bethe Ansatz for the phase model
• Lattice polarized toric K3 surfaces
• Equivariant Verlinde formula from fivebranes and vortices
• Families of lattice polarized K3 surfaces with monodromy
• Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
• Rational curves on Calabi-Yau threefolds

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• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Lectures on AdS Black Holes, Holography and Localization
• 5d Partition Functions with A Twist
• A gravity interpretation for the Bethe Ansatz expansion of the $\mathcal{N}=4$ SYM index
• Superconformal indices at large $N$ and the entropy of AdS${}_5$ $\times$ SE${}_5$ black holes
• Rational $Q$-systems, Higgsing and Mirror Symmetry
• Twisted Hilbert Spaces of 3d Supersymmetric Gauge Theories
• Large $N$ Superconformal Indices for 3d Holographic SCFTs
• One-loop determinants for black holes in 4d gauged supergravity
• The Topologically Twisted Index in the 't Hooft Limit and the Dual AdS${}_4$ Black Hole Entropy
• Holonomy Saddles and Supersymmetry
• A-twisted correlators and Hori dualities
• Calabi-Yau Threefolds Fibred by Mirror Quartic K3 Surfaces
• Factorising the 3D Topologically Twisted Index
• $\mathcal{I}$/$c$-Extremization in M/F-Duality
• Magnetic charge and black hole supersymmetric quantum statistical relation
• A non-unitary bulk-boundary correspondence: Non-unitary Haagerup RCFTs from S-fold SCFTs
• Deconstructing Little Strings with $\mathcal{N}=1$ Gauge Theories on Ellipsoids
• Subleading Microstate Counting in the Dual to Massive Type IIA
• Supersymmetric AdS${}_2\times {\Sigma }_2$ solutions from tri-sasakian truncation
• Perverse sheaves of categories and some applications
• The large-$N$ limit of 4d superconformal indices for general BPS charges
• On the Witten index of 3d $\mathcal{N}=2$ unitary SQCD with general CS levels
• Doran-Harder-Thompson Conjecture via SYZ Mirror Symmetry: Elliptic Curves
• Duality invariance in Fayet-Iliopoulos gauged supergravity
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• Supersymmetric ground states of 3d $\mathcal{N}=4$ SUSY gauge theories and Heisenberg Algebras
• Topologically Twisted SUSY Gauge Theory, Gauge-Bethe Correspondence and Quantum Cohomology
• Non-hyperbolic 3-manifolds and 3D field theories for 2D Virasoro minimal models
• One-form symmetries and the 3d $\mathcal{N}=2$ $A$-model: Topologically twisted indices and CS theories
• Degenerations and Lagrangian fibrations of Calabi-Yau manifolds
• Holography for $\mathcal{N}=1^{\ast }$ on $S^4$ and Supergravity
• Affine elliptic surfaces with type-A singularities and orbi-conifolds
• Towards the Doran-Harder-Thompson conjecture via the Gross-Siebert program