تقرير
Categorified Open Topological Field Theories
| العنوان: | Categorified Open Topological Field Theories |
|---|---|
| المؤلفون: | Müller, Lukas, Woike, Lukas |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Quantum Algebra, Mathematical Physics, Mathematics - Algebraic Topology |
| الوصف: | In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories. In combination with recently developed string-net techniques, this leads to a new description of the spaces of conformal blocks of Drinfeld centers $Z(\mathcal{C})$ of pivotal finite tensor categories $\mathcal{C}$ in terms of the modular envelope of the cyclic associative operad. If $\mathcal{C}$ is unimodular, we prove that the space of conformal blocks inherits the structure of a module over the algebra of class functions of $\mathcal{C}$ for every free boundary component. As a further application, we prove that the sewing along a boundary circle for the modular functor for $Z(\mathcal{C})$ can be decomposed into a sewing procedure along an interval and the application of the partial trace. Finally, we construct mapping class group representations from Grothendieck-Verdier categories that are not necessarily rigid and make precise how these generalize existing constructions. Comment: 14 pages, some diagrams |
| نوع الوثيقة: | Working Paper |
| الوصول الحر: | http://arxiv.org/abs/2406.11605Test |
| رقم الانضمام: | edsarx.2406.11605 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |