2d Partition Function in Omega-background and Vortex/Instanton Correspondence

Abstract

We derive the exact vortex partition function in 2d $\mathcal{N}$ = (2,2) gauge theory on the Omega-background, applying the localization scheme in the Higgs phase. We show that the partition function at a finite Omega-deformation parameter $\epsilon$ satisfies a system of differential equations, which can be interpreted as a quantized version of the twisted F-term equations characterizing the SUSY vacua. Using the differential equations derived in this paper, we show the correspondence between the partition function of the two-dimensional vortex string worldsheet theory and the Nekrasov partition function at the root of Higgs branch of the four-dimensional $\mathcal{N}$ = 2 theory with two Omega-deformation parameters $({\epsilon }_1,{\epsilon }_2)$.

1+45 pages, 7 figures; typos corrected, references added

References in corpus (15)

• Supersymmetric Solitons and How They Help Us Understand Non-Abelian Gauge Theories
• Instantons in the Higgs Phase
• TASI Lectures on Solitons
• Seiberg-Witten prepotential from instanton counting
• Intersecting Solitons, Amoeba and Tropical Geometry
• Fractional Vortices and Lumps
• Non-Abelian Monopoles in the Higgs Phase
• ADE Little String Theory on a Riemann Surface (and Triality)
• Heterotic Surface Defects and Dualities from 2d/4d Indices
• Virasoro constraint for Nekrasov instanton partition function
• Ellipsoid partition function from Seiberg-Witten monopoles
• Vortex counting from field theory
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• Spherical Hecke algebra in the Nekrasov-Shatashvili limit

Cited by in corpus (11)

• Relations among topological solitons
• Supersymmetric localization in two dimensions
• Localization of 4d $\mathcal{N}=1$ theories on ${\mathbb{D}}^2\times {\mathbb{T}}^2$
• Intersecting Defects and Supergroup Gauge Theory
• Quiver ${\text{W}}_{{\epsilon }_1,{\epsilon }_2}$ algebras of 4d $\mathcal{N}=2$ gauge theories
• Elliptic Genus Derivation of 4d Holomorphic Blocks
• Phase Transition of the Horava-Lifshitz AdS black holes
• Boundary Weyl anomaly of $\mathcal{N}=(2,2)$ superconformal models
• Partition Functions of $\mathcal{N}=1$ Gauge Theories on $S^2\times {\mathbb{R}}_{\epsilon }^2$ and Duality
• Les Houches lectures on non-perturbative Seiberg-Witten geometry
• Difference Equations: from Berry Connections to the Coulomb Branch