{
"id": "2002.05716",
"version": "v1",
"published": "2020-02-13T18:56:55.000Z",
"updated": "2020-02-13T18:56:55.000Z",
"title": "Ungauging Schemes and Coulomb Branches of Non-simply Laced Quiver Theories",
"authors": [
"Amihay Hanany",
"Anton Zajac"
],
"comment": "21 pages",
"categories": [
"hep-th"
],
"abstract": "Three dimensional Coulomb branches have a prominent role in the study of moduli spaces of supersymmetric gauge theories with $8$ supercharges in $3,4,5$, and $6$ dimensions. Inspired by simply laced \\3d supersymmetric quiver gauge theories, we consider Coulomb branches constructed from non-simply laced quivers with edge multiplicity $k$ and no flavor nodes. In a computation of the Coulomb branch as the space of dressed monopole operators, a center-of-mass $U(1)$ symmetry needs to be ungauged. Typically, for a simply laced theory, all choices of the ungauged $U(1)$ (i.e. all choices of \\emph{ungauging schemes}) are equivalent and the Coulomb branch is unique. In this note, we study various ungauging schemes and their effect on the resulting Coulomb branch variety. It is shown that, for a non-simply laced quiver, inequivalent ungauging schemes exist which correspond to inequivalent Coulomb branch varieties. Ungauging on any of the long nodes of a non-simply laced quiver yields the same Coulomb branch $\\mathcal{C}$. For choices of ungauging the $U(1)$ on a short node of rank higher than $1$, the GNO dual magnetic lattice deforms such that it no longer corresponds to a Lie group, and therefore, the monopole formula yields a non-valid Coulomb branch. However, if the ungauging is performed on a short node of rank $1$, the one-dimensional magnetic lattice is rescaled conformally along its single direction and the corresponding Coulomb branch is an orbifold of the form $\\mathcal{C}/\\mathbb{Z}_k$. Ungauging schemes of $3$d Coulomb branches provide a particularly interesting and intuitive description of a subset of actions on the nilpotent orbits studied by Kostant and Brylinski \\cite{KB92}. The ungauging scheme analysis is carried out for minimally unbalanced $C_n$, affine $F_4$, affine $G_2$, and twisted affine $D_4^{(3)}$ quivers, respectively.",
"revisions": [
{
"version": "v1",
"updated": "2020-02-13T18:56:55.000Z"
}
],
"analyses": {
"keywords": [
"ungauging scheme",
"non-simply laced quiver theories",
"coulomb branch variety",
"gno dual magnetic lattice deforms",
"short node"
],
"note": {
"typesetting": "TeX",
"pages": 21,
"language": "en",
"license": "arXiv",
"status": "editable"
}
}
}