تقرير
Topological-Holomorphic ${\mathcal N} =4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-topological Strings
| العنوان: | Topological-Holomorphic ${\mathcal N} =4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-topological Strings |
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| المؤلفون: | Ong, Zhi-Cong, Tan, Meng-Chwan |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics High Energy Physics - Theory |
| مصطلحات موضوعية: | High Energy Physics - Theory, Mathematics - Algebraic Geometry, Mathematics - Differential Geometry, Mathematics - Quantum Algebra, Mathematics - Representation Theory |
| الوصف: | We perform a topological-holomorphic twist of $\mathcal{N}=4$ supersymmetric gauge theory on a four-manifold of the form $M_4=\Sigma_1 \times \Sigma_2$ with Riemann surfaces $\Sigma_{1,2}$, and unravel the mathematical implications of its physics. In particular, we consider different linear combinations of the resulting scalar supercharges under $S$-duality, where this will allow us to derive novel topological and holomorphic invariants of $M_4$ and their Langlands duals. As the twisted theory can be topological along $\Sigma_1$ whence we can dimensionally reduce it to 2d, via the effective sigma-model on $\Sigma_2$, we can also relate these 4d invariants and their Langlands duals to the mirror symmetry of Higgs bundles and that of quasi-topological strings described by the sheaf of chiral differential operators. As an offshoot, we would be able to obtain a fundamental understanding from 4d gauge theory, why chiral differential operators are purely perturbative objects. Comment: 30 pp. Further clarifications |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2305.15965 |
| رقم الأكسشن: | edsarx.2305.15965 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |