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Vacua, Symmetries, and Higgsing of Chern-Simons Matter Theories
by Fabio Marino, Marcus Sperling
Submission summary
| Authors (as registered SciPost users): | Marcus Sperling |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2503.02744v1 (pdf) |
| Date submitted: | 2025-03-10 13:58 |
| Submitted by: | Sperling, Marcus |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Three-dimensional supersymmetric Chern-Simons Matter (CSM) theories typically preserve $ \mathcal{N}=3$ supersymmetry but can exhibit enhanced $\mathcal{N}=4$ supersymmetry under special conditions. A detailed understanding of the moduli space of CSM theories, however, has remained elusive. This paper addresses this gap by systematically analysing the maximal branches of the moduli space of $\mathcal{N}=3$ and $\mathcal{N}=4$ CSM realised via Type IIB brane constructions. Firstly, for $\mathcal{N}=4$ theories with Chern-Simons levels equal $1$, the $\mathrm{SL}(2,\mathbb{Z})$ dualisation algorithm is employed to construct dual Lagrangian 3d $\mathcal{N}=4$ theories without CS terms. This allows the full moduli space to be determined using quiver algorithms that compute Higgs and Coulomb branch Hasse diagrams and associated RG flows. Secondly, for $\mathcal{N}=4$ theories with CS-levels greater $1$, where $\mathrm{SL}(2,\mathbb{Z})$ dualisation does not yield CS-free Lagrangians, a new prescription is introduced to derive two magnetic quivers, $\mathsf{MQ}_A $ and $\mathsf{MQ}_B$, whose Coulomb branches capture the maximal A and B branches of the original $\mathcal{N}=4$ CSM theory. Applying the decay and fission algorithm to $ \mathsf{MQ}_{A/B}$ then enables the systematic analysis of A/B branch RG flows and their geometric structures. Thirdly, for $\mathcal{N}=3$ CSM theories, one magnetic quiver for each maximal (hyper-K\"ahler) branch is derived from the brane system. This provides an efficient and comprehensive characterisation of these previously scarcely studied features.
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