Coulomb branches for quaternionic representations
Abstract
I describe the \emph{Chiral rings} $R_{3,4}$ for $3$D, $N=4$ supersymmetric $G$gauge theory and matter fields in quaternionic representations $E$: first, by a topological tweak of the construction of arxiv:1601.03586, and second, more explicitly, by Weyl group descent from the maximal torus. A topological obstruction is $w_4(E)$ modulo squares, for $R_3$; a secondary obstruction, from $\eta\cdot E$, may appear for $R_4$. Flatness over the Toda bases allows their calculation by reduction to $\mathrm{SU}_2$. For some representations, an Abelianization formula describes the $R$ in terms of the maximal torus and the Weyl group. This provides an alternative to a recent attempt arxiv:2201.09475.
 Publication:

arXiv eprints
 Pub Date:
 September 2022
 DOI:
 10.48550/arXiv.2209.01088
 arXiv:
 arXiv:2209.01088
 Bibcode:
 2022arXiv220901088T
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematical Physics;
 55N91;
 22E46;
 81T13
 EPrint:
 V.3 adds an explicit description in terms of the maximal torus and Weyl group.. V.2 corrected the topology result (secondary obstruction) and some calculations in the appendix, and added Edits and clarifications