更高超空间超引力及其红外完备化
Higher Superspace Supergravity and its IR-Completions
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中文总结 AI 辅助
研究高维超引力的红外完备化，通过在微分非阿贝尔上同调理论中对电磁通量量子化来构建。阐述了相关背景及成果，包括11维、10维IIA超引力及M5膜世界体积的情况，意味着可对多种超引力进行一致的红外完备化及拓扑量子序几何工程。
中文摘要 AI 辅助
一个古老的观点认为，通过在受超挠率约束的超时空上对超场强施加比安基恒等式，就可以使高维超引力（SuGra）处于壳上。我们给出了一个现代化的、严谨的阐述并回顾了近期的发展，指出这种观点如何通过微分非阿贝尔上同调理论\(\mathcal{A}_{\mathrm{dff}}\)中的电磁通量量子化来构建SuGra的红外完备化，提升超比安基恒等式的系数\(L_\infty\)-代数\(\mathfrak{l}\mathcal{A}\)。在概述必要背景后，我们强调：（1）我们最近证明11维SuGra的解等同于无超挠率的11维超时空上超\(C\)-场通量的\(\mathfrak{l}S^4\)-比安基恒等式；（2）由此6维M5膜世界体积上的非线性自对偶规范扇区等同于超\(B\)-场通量的\(\mathfrak{l}_{S^4}S^7\)-比安基恒等式；（3）以及近期通过超NS/RR通量的\(\mathfrak{l}\mathrm{Cyc}(S^4)\)-比安基恒等式将这种情况超空间降维到10维IIA SuGra的完整讨论，及其通过相应超通量的\(\mathfrak{l}\mathrm{Tor}(S^4)\)-比安基恒等式进一步降维到9维超引力的扩展。最后我们指出这意味着通过4-同伦中的\(C\)-场通量量子化对11维SuGra、通过扭曲不稳定\(K\)-理论形式的NS/RR场通量量子化对10维IIA SuGra以及通过扭曲（扭量）相对同伦中的\(B\)-场通量量子化对M5膜世界体积进行一致的红外完备化。后者允许对实验相关的拓扑量子序进行几何工程。
英文摘要
It is an old idea that higher-dimensional super-gravity (SuGra) is put on-shell just by imposing Bianchi identities on super-field strengths over super-spacetimes subject to super-torsion constraints. We give a modernized, rigorous account and review recent developments, pointing out how this perspective lends itself to the construction of infrared completions of SuGra by electromagnetic flux quantization in differential nonabelian cohomology theories $\mathcal{A}_{\mathrm{dff}}$ lifting the coefficient $L_\infty$-algebra $\mathfrak{l}\mathcal{A}$ of the super-Bianchi identities. After surveying necessary background, we highlight: (1.) our recent proof that solutions of 11D SuGra are equivalent to the $\mathfrak{l}S^4$-Bianchi identities on super $C$-field flux over super-torsion-free 11D super-spacetimes, (2.) how from this the nonlinearly self-dual gauge sector on 6D M5-brane worldvolumes is equivalent to the $\mathfrak{l}_{S^4}S^7$-Bianchi identity on super $B$-field flux, (3.) and the recent complete discussion of superspace dimensional reduction of this situation to 10D IIA SuGra via $\mathfrak{l}\mathrm{Cyc}(S^4)$-Bianchi identities on super NS/RR-flux, together with its extension to further reduction to 9 SuGra via $\mathfrak{l}\mathrm{Tor}(S^4)$-Bianchis on the corresponding super-fluxes. We close by indicating how this implies consistent infrared completions of 11D SuGra by $C$-field flux quantization in 4-Cohomotopy, of 10D IIA SuGra by NS/RR-field flux-quantization in a form of twisted unstable K-theory, and of M5-brane worldvolumes by $B$-field flux-quantization in twisted (twistorial) relative Cohomotopy. The latter admits geometric engineering of experimentally relevant topological quantum orders.
