Partition functions of N=(2,2) gauge theories on S^2 and vortices

Abstract

We apply localization techniques to compute the partition function of a two-dimensional N=(2,2) R-symmetric theory of vector and chiral multiplets on S^2. The path integral reduces to a sum over topological sectors of a matrix integral over the Cartan subalgebra of the gauge group. For gauge theories which would be completely Higgsed in the presence of a Fayet-Iliopoulos term in flat space, the path integral alternatively reduces to the product of a vortex times an antivortex partition functions, weighted by semiclassical factors and summed over isolated points on the Higgs branch. As applications we evaluate the partition function for some U(N) gauge theories, showing equality of the path integrals for theories conjectured to be dual by Hori and Tong and deriving new expressions for vortex partition functions.

62 pages + 16 of appendices; v2: minor modifications, refs added; v3: typos corrected, ref added

References in corpus (18)

• Notes on SUSY Gauge Theories on Three-Sphere
• Exact Results in D=2 Supersymmetric Gauge Theories
• Webs of five-branes and N=2 superconformal field theories
• Four-Dimensional SCFTs from M5-Branes
• Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
• Mirrors of 3d Sicilian theories
• Tinkertoys for Gaiotto Duality
• Supersymmetric Gauge Theories on the Five-Sphere
• TASI Lectures on Solitons
• Correlation functions in conformal Toda field theory I
• Generalized Superconformal Index for Three Dimensional Field Theories
• Seiberg-Witten Theory and Random Partitions
• Superconformal indices of three-dimensional theories related by mirror symmetry
• Nonabelian 2D Gauge Theories for Determinantal Calabi-Yau Varieties
• Seiberg-Witten prepotential from instanton counting
• Relating Gauge Theories via Gauge/Bethe Correspondence
• Vortex counting from field theory
• Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory

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