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| Main Author: | |
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| Format: | Preprint |
| Published: |
2018
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1801.10124 |
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Table of Contents:
- I give a simple construction of certain Coulomb branches $C_{3,4}(G;E)$ of gauge theory in 3 and 4 dimensions defined by Nakajima et al. for a compact Lie group $G$ and a polarisable quaternionic representation $E$. The manifolds $C(G; 0)$ are abelian group schemes (over the bases of regular adjoint $G_c$-orbits, respectively conjugacy classes), and $C(G;E)$ is glued together from two copies of $C(G;0)$ shifted by a rational Lagrangian section $\varepsilon_V$, the Euler class of the index bundle of a polarisation $V$ of $E$. Extending the interpretation of $C_3(G;0)$ as "classifying space" for topological 2D gauge theories, I characterise functions on $C_3(G;E)$ as operators on the equivariant quantum cohomologies of $M\times V$, for all compact symplectic $G$-manifolds $M$. The non-commutative version has an analogous description in terms of the $Γ$-function of $V$, appearing to play the role of Fourier transformed J-function of the gauged linear Sigma-model $V/G$.