Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2018
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/1801.10124 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908631423778816 |
|---|---|
| author | Teleman, Constantin |
| author_facet | Teleman, Constantin |
| 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 $V/G$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1801_10124 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | The role of Coulomb branches in 2D gauge theory Teleman, Constantin Algebraic Geometry High Energy Physics - Theory Algebraic Topology 55N91, 81R05, 81R12 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 $V/G$. |
| title | The role of Coulomb branches in 2D gauge theory |
| topic | Algebraic Geometry High Energy Physics - Theory Algebraic Topology 55N91, 81R05, 81R12 |
| url | https://arxiv.org/abs/1801.10124 |