Holomorphic Blocks for 3d Non-abelian Partition Functions

Abstract

The most recent studies on the supersymmetric localization reveal many non-trivial features of supersymmetric field theories in diverse dimensions, and 3d gauge theory provides a typical example. It was conjectured that the index and the partition function of a 3d N=2 theory are constructed from a single component: the holomorphic block. We prove this conjecture for non-abelian gauge theories by computing exactly the 3d partition functions and holomorphic blocks.

24 pages, 4 figures

References in corpus (18)

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• Partition functions of N=(2,2) gauge theories on S^2 and vortices
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Cited by in corpus (24)

• Higgs branch localization in three dimensions
• Dual Boundary Conditions in 3d SCFT's
• Higgs branch localization of 3d N=2 theories
• Higgs branch localization of $\mathcal{N}=1$ theories on $S^3\times S^1$
• Universal 3d Cardy Block and Black Hole Entropy
• Gauge/Liouville Triality
• Factorization of S^3/Z_n partition function
• Holomorphic blocks and the 5d AGT correspondence
• Quantum vortices, M2-branes and black holes
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Fundamental Vortices, Wall-Crossing, and Particle-Vortex Duality
• The Stringy Instanton Partition Function
• Factorization of 4d N=1 superconformal index
• Ω-deformation of B-twisted gauge theories and the 3d-3d correspondence
• Supersymmetric index on T^2 x S^2 and elliptic genus
• Basic hypergeometry of supersymmetric dualities
• 3d Mirror Symmetry from S-duality
• Connecting Mirror Symmetry in 3d and 2d via Localization
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• Abelian 3d mirror symmetry on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ with $N_f=1$
• Bootstrapping the $S^5$ partition function
• Wilson loops and free energies in $3d$ $\mathcal{N}=4$ SYM: exact results, exponential asymptotics and duality
• Non-Perturbative Schwinger-Dyson Equations for 3d $\mathcal{N}=4$ Gauge Theories
• Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories