S^3/Z_n partition function and dualities

Abstract

We investigate S^3/Z_n partition function of N = 2 supersymmetric gauge theories. A gauge theory on the orbifold has degenerate vacua specified by the holonomy. The partition function is obtained by summing up the contributions of saddle points with different holonomies. An appropriate choice of the phase of each contribution is essential to obtain the partition function. We determine the relative phases in the holonomy sum in a few examples by using duality to non-gauge theories. In the case of odd n the phase factors can be absorbed by modifying a single function appearing in the partition function.

30 pages, 2 figures, added references

References in corpus (10)

• N=6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
• Notes on SUSY Gauge Theories on Three-Sphere
• Quantization of models with non-compact quantum group symmetry. Modular XXZ magnet and lattice sinh-Gordon model
• Generalized Superconformal Index for Three Dimensional Field Theories
• Faddeev-Volkov solution of the Yang-Baxter Equation and Discrete Conformal Symmetry
• Black Holes, Instanton Counting on Toric Singularities and q-Deformed Two-Dimensional Yang-Mills Theory
• Seiberg-like duality in three dimensions for orthogonal gauge groups
• A Duality Appetizer
• Refined Checks and Exact Dualities in Three Dimensions
• Reshetikhin-Turaev invariants of Seifert 3-manifolds for classical simple Lie algebras, and their asymptotic expansions

Cited by in corpus (34)

• 3d dualities from 4d dualities
• Seifert fibering operators in 3d $\mathcal{N}=2$ theories
• Higgs branch localization of 3d N=2 theories
• Factorisation and holomorphic blocks in 4d
• Localization on three-dimensional manifolds
• Cardy Formula for 4d SUSY Theories and Localization
• Factorization of S^3/Z_n partition function
• The star-triangle relation, lens partition function, and hypergeometric sum/integrals
• How to resum perturbative series in 3d N=2 Chern-Simons matter theories
• Non-unitary TQFTs from 3D $\mathcal{N}=4$ rank 0 SCFTs
• Superconformal Index and 3d-3d Correspondence for Mapping Cylinder/Torus
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• $q$-Virasoro modular double and 3d partition functions
• Basic hypergeometry of supersymmetric dualities
• A matrix model for the latitude Wilson loop in ABJM theory
• AGT/Z${}_2$
• A review on SUSY gauge theories on $S^3$
• Superconformal index on ${\mathbb{RP}}^2\times {\mathbb{S}}^1$ and mirror symmetry
• Integrable lattice spin models from supersymmetric dualities
• 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 $N_f=1$
• From rarefied elliptic beta integral to parafermionic star-triangle relation
• A parafermionic hypergeometric function and supersymmetric 6j-symbols
• Complex Chern-Simons theory at level k via the 3d-3d correspondence
• Lens partition function, pentagon identity and star-triangle relation
• Hyperbolic and trigonometric hypergeometric solutions to the star-star equation
• General modular quantum dilogarithm and beta integrals
• Pentagon identities arising in supersymmetric gauge theory computations
• On Bailey pairs for $\mathcal{N}=2$ supersymmetric gauge theories on $S_b^3/{\mathbb{Z}}_r$
• S-move matrix in the NS sector of $N=1$ super Liouville field theory
• A journey to 3d: exact relations for adjoint SQCD from dimensional reduction
• From $\mathcal{N}=4$ Super-Yang-Mills on ${\mathbb{RP}}^4$ to bosonic Yang-Mills on ${\mathbb{RP}}^2$
• Topological phase, spin Chern-Simons theory and level rank duality on lens space
• Anomalies and Holomorphy in Supersymmetric Chern-Simons-Matter Theories