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3d $\mathcal{N}=$ 4 rank-0 SCFT from punctured lens space
Sungjoon Kim
https://arxiv.org/abs/2608.13300 https://arxiv.org/pdf/2608.13300 https://arxiv.org/html/2608.13300
arXiv:2608.13300v1 Announce Type: new
Abstract: {\it Gang-Kim-Stubbs} theory $\mathcal{T}_n$ --- a pioneering 3d bulk description of $M(2n 3,2)$ Virasoro minimal model as $\mathcal{N}=4$ rank-0 superconformal field theory upon topological A-twist --- is derived from the compactification of a pair of parallel M5-branes on {\it lens space} $L(2n 3,2)$ with a single vertex removed. From this perspective, we propose a family of 3d $\mathcal{N}=2$ abelian gauge theories arising from the punctured $L(2n 3,1)$ lens space whose infrared phases realize the unitary member in the Galois orbit of $M(2n 3,2)$ modular tensor category. We also conjecture self-mirror rank-0 fixed points from amphichirality condition of the lens space.
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Representability of continuous K-theory in rigid analytic motivic $\mathbb{A}^1$-homotopy theory
Christian Dahlhausen, Can Yaylali, Yicheng Zhou
https://arxiv.org/abs/2608.06209 https://arxiv.org/pdf/2608.06209 https://arxiv.org/html/2608.06209
arXiv:2608.06209v1 Announce Type: new
Abstract: We prove that both continuous K-theory and analytic K-theory of rigid analytic spaces (\`a la Kerz--Saito--Tamme) satisfiy descent with respect to the Nisnevich topology. Together with the fact that it is $\mathbb{A}^1$-invariant assuming resolutions of singularities, we deduce that it is representable in the $\mathbb{A}^{1}$-homotopy category of rigid spaces (\`a la Dahlhausen--Yaylali). We identifiy the representing object with both $\mathbb{Z}\times\mathrm{BGL}$ and the analytification of algebraic K-theory. As a consequence, we get a representability statement for coefficients in light condensed spectra. Moreover, we show Weibel vanishing and that continuous K-theory is $\mathbb{A}^1$-invariant on local Tate pairs (without any regularity assumption).
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[2026-07-24 Fri (UTC), no new articles found for math.CT Category Theory]
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[2026-07-23 Thu (UTC), 3 new articles found for math.CT Category Theory]
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[2026-07-22 Wed (UTC), no new articles found for math.CT Category Theory]
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[2026-07-21 Tue (UTC), 3 new articles found for math.CT Category Theory]
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Crosslisted article(s) found for math.CT. https://arxiv.org/list/math.CT/new
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- Fibrations in Oriented Category Theory
David Gepner, Hadrian Heine
https:/…