تقرير
Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with $\mathcal{N}=4$ Symmetry
| العنوان: | Hilbert Schemes of Points in the Plane and Quasi-Lisse Vertex Algebras with $\mathcal{N}=4$ Symmetry |
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| المؤلفون: | Arakawa, Tomoyuki, Kuwabara, Toshiro, Möller, Sven |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | Mathematics - Representation Theory, High Energy Physics - Theory, Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, 17B69, 81T60, 17B67, 17B63 |
| الوصف: | To each complex reflection group $\Gamma$ one can attach a canonical symplectic singularity $\mathcal{M}_\Gamma$ arXiv:math/9903070. Motivated by the 4D/2D duality arXiv:1312.5344, arXiv:1707.07679, Bonetti, Meneghelli and Rastelli arXiv:1810.03612 conjectured the existence of a supersymmetric vertex operator superalgebra $\mathsf{W}_\Gamma$ whose associated variety is isomorphic to $\mathcal{M}_\Gamma$. We prove this conjecture when the complex reflection group $\Gamma$ is the symmetric group $S_N$ by constructing a sheaf of $\hbar$-adic vertex operator superalgebras on the Hilbert scheme of $N$ points in the plane. For that case, we also show the free-field realisation of $\mathsf{W}_\Gamma$ in terms of $\operatorname{rk}(\Gamma)$ many $\beta\gamma bc$-systems proposed in arXiv:1810.03612, and identify the character of $\mathsf{W}_\Gamma$ as a certain quasimodular form of mixed weight and multiple $q$-zeta value. In physical terms, the vertex operator superalgebra $\mathsf{W}_{S_N}$ constructed in this article corresponds via the 4D/2D duality arXiv:1312.5344 to the four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory with gauge group $\operatorname{SL}_N$. Comment: 58 pages, LaTeX; improvements to the exposition, added many references, added subsection on multiple $q$-zeta values |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2309.17308 |
| رقم الأكسشن: | edsarx.2309.17308 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |