Positive Traces on Certain ${\rm SL}(2)$ Coulomb Branches

[2507.19447] Positive Traces on Certain ${\rm SL}(2)$ Coulomb Branches Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search High Energy Physics - Theory arXiv:2507.19447 (hep-th) [Submitted on 25 Jul 2025 ( v1 ), last revised 10 Apr 2026 (this version, v2)] Title: Positive Traces on Certain ${\rm SL}(2)$ Coulomb Branches Authors: Daniil Klyuev , Joseph Vulakh View a PDF of the paper titled Positive Traces on Certain ${\rm SL}(2)$ Coulomb Branches, by Daniil Klyuev and 1 other authors View PDF HTML (experimental) Abstract: For a noncommutative algebra $\mathcal{A}$ and an antilinear automorphism $\rho$ of $\mathcal{A}$, there is a notion of a positive trace. When we have a three-dimensional $\mathcal{N}=4$ gauge theory or four-dimensional $\mathcal{N}=2$ gauge theory compactified on a circle, classification of positive traces on its Coulomb branch $\mathcal{A}$ can give a better understanding of this theory. We classify positive traces on $\mathcal{A}$ in two cases. The first case is when $\mathcal{A}$ is a quantization of a Kleinian singularity of type $D$, with certain restriction on the quantization parameter. The second case is when $\mathcal{A}=K^{{\rm SL}(2,\mathbb{C}[[t]])\rtimes \mathbb{C}_q^{\times}}({\rm Gr}_{{\rm PGL}_2})$ is an algebra containing $K$-theoretic Coulomb branches of pure ${\rm SL}(2)$ and ${\rm PGL}(2)$ gauge theories. Subjects: High Energy Physics - Theory (hep-th) ; Mathematical Physics (math-ph); Representation Theory (math.RT) Cite as: arXiv:2507.19447 [hep-th] (or arXiv:2507.19447v2 [hep-th] for this version) https://doi.org/10.48550/arXiv.2507.19447 Focus to learn more arXiv-issued DOI via DataCite Journal reference: SIGMA 22 (2026), 033, 34 pages Related DOI : https://doi.org/10.3842/SIGMA.2026.033 Focus to learn more DOI(s) linking to related resources Submission history From: Daniil Klyuev [ view email ] [via Journal Sigma as proxy] [v1] Fri, 25 Jul 2025 17:28:04 UTC (33 KB) [v2] Fri, 10 Apr 2026 19:32:13 UTC (37 KB) Full-text links: Access Paper: View a PDF of the paper titled Positive Traces on Certain ${\rm SL}(2)$ Coulomb Branches, by Daniil Klyuev and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: hep-th < prev | next > new | recent | 2025-07 Change to browse by: math math-ph math.MP math.RT References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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