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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 | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.02744v2 (pdf) |
| Date accepted: | May 12, 2025 |
| Date submitted: | April 25, 2025, 2:13 p.m. |
| Submitted by: | Sperling, Marcus |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| 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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
- clarified axial charge convention; added Table 4 to specify multiplets read off from brane intersections
- improved presentation of Abelian N=3 Chern-Simons matter theories sections
- added new sections on non-Abelian N=3 Chern-Simons matter theories
- added Figure 23 to explain the strategy for deriving magnetic quivers for each maximal branch in N=3 theories
- revised and expanded introduction, to emphasise motivation
- fixed typos
Current status:
Editorial decision:
For Journal SciPost Physics: Publish
(status: Editorial decision fixed and (if required) accepted by authors)
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As a side comment, the newly added find Table 4 very neat. It is certainly true that the previous conventions did not alter the final results, but I believe the current version using the most common convention for hypers vs twisted hypers will be of easier access for the readers.
Overall I consider the paper worth publishing in SciPost Physics in the current version.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)