Moduli spaces of framed symplectic and orthogonal bundles on P2 and the K-theoretic Nekrasov partition functions

Abstract

Let $K$ be the compact Lie group $USp(N/2)$ or $SO(N,R)$. Let $M_n^K$ be the moduli space of framed K-instantons over $S^4$ with the instanton number $n$. By Donaldson (1984), $M_n^K$ is endowed with a natural scheme structure. It is a Zariski open subset of a GIT quotient of ${\mu }^{-1}(0)$, where $\mu$ is a holomorphic moment map such that ${\mu }^{-1}(0)$ consists of the ADHM data. The purpose of the paper is to study the geometric properties of ${\mu }^{-1}(0)$ and its GIT quotient, such as complete intersection, irreducibility, reducedness and normality. If $K=USp(N/2)$ then $\mu$ is flat and ${\mu }^{-1}(0)$ is an irreducible normal variety for any $n$ and even $N$. If $K=SO(N,R)$ the similar results are proven for low $n$ and $N$. As an application one can obtain a mathematical interpretation of the K-theoretic Nekrasov partition function of Nekrasov and Shadchin (2004).

32 pages, 1 figure; 7 pages (corrigendum and addendum)

References in corpus (7)

• Monopole Condensation, And Confinement In N=2 Supersymmetric Yang-Mills Theory
• Five Dimensional Gauge Theories and Relativistic Integrable Systems
• Quantum Groups and Quantum Cohomology
• ABCD of instantons
• The Hilbert Series of the One Instanton Moduli Space
• From SO/Sp instantons to W-algebra blocks
• K-theoretic Donaldson invariants via instanton counting

Cited by in corpus (3)

• Towards a mathematical definition of Coulomb branches of $3$-dimensional $\mathcal{N}=4$ gauge theories, II
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