Localization of Vortex Partition Functions in $\mathcal{N}=(2,2)$ Super Yang-Mills theory

Abstract

In this article, we study the localizaiton of the partition function of BPS vortices in $\mathcal{N}=(2,2)$ $U(N)$ super Yang-Mills theory with $N$-flavor on ${\mathbb{R}}^2$. The vortex partition function for $\mathcal{N}=(2,2)$ super Yang-Mills theory is obtained from the one in $\mathcal{N}=(4,4)$ super Yang-Mills theory by mass deformation. We show that the partition function can be written as $Q$-exact form and integration in the partition functions is localized to the fixed points which are related to $N$-tuple one dimensional partitions of positive integers.

15 pages

References in corpus (10)

• The Refined Topological Vertex
• Solitons in the Higgs phase -- the moduli matrix approach --
• D-particle bound states and generalized instantons
• Vortex Counting and Lagrangian 3-manifolds
• NS5-Branes, T-Duality and Worldsheet Instantons
• A & B model approaches to surface operators and Toda theories
• Heterotic Vortex Strings
• Instantons and Emergent AdS_3 x S^3 Geometry
• The $S^1$ fixed points in Quot-schemes and mirror principle computations
• Two Proofs of a Conjecture of Hori and Vafa

Cited by in corpus (12)

• Partition functions of N=(2,2) gauge theories on S^2 and vortices
• Exact Results in D=2 Supersymmetric Gauge Theories
• Defects and Quantum Seiberg-Witten Geometry
• Elliptic hypergeometry of supersymmetric dualities II. Orthogonal groups, knots, and vortices
• Vertices, Vortices & Interacting Surface Operators
• Higgs branch localization of 3d N=2 theories
• The Quantum Hall Effect in Supersymmetric Chern-Simons Theories
• Factorization of 4d N=1 superconformal index
• 2d Partition Function in Omega-background and Vortex/Instanton Correspondence
• On Higgs Branch Localization of Seiberg-Witten Theories on Ellipsoid
• On Integrable Structure and Geometric Transition in Supersymmetric Gauge Theories
• Orbifold Vortex and Super Liouville Theory