Hilbert Series and Moduli Spaces of k U(N) Vortices

Abstract

We study the moduli spaces of k U(N) vortices which are realized by the Higgs branch of a U(k) supersymmetric gauge theory. The theory has 4 supercharges and lives on k D1-branes in a N D3- and NS5-brane background. We realize the vortex moduli space as a C* projection of the vortex master space. The Hilbert series is calculated in order to characterize the algebraic structure of the vortex master space and to identify the precise C* projection. As a result, we are able to fully classify the moduli spaces up to 3 vortices.

102 pages, 8 figures, 5 tables

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Cited by in corpus (4)

• Hilbert Series for Constructing Lagrangians: expanding the phenomenologist's toolbox
• Constructing Operator Basis in Supersymmetry: A Hilbert Series Approach
• Counting Operators in $N=1$ Supersymmetric Gauge Theories
• The ADHM-like Constructions for Instantons on CP^2 and Three Dimensional Gauge Theories