Topological-Holomorphic ${\mathcal N} =4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-topological Strings
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866916265431400448 |
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| author | Ong, Zhi-Cong Tan, Meng-Chwan |
| author_facet | Ong, Zhi-Cong Tan, Meng-Chwan |
| contents | We perform a topological-holomorphic twist of $\mathcal{N}=4$ supersymmetric gauge theory on a four-manifold of the form $M_4=Σ_1 \times Σ_2$ with Riemann surfaces $Σ_{1,2}$, 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 $Σ_1$ whence we can dimensionally reduce it to 2d, via the effective sigma-model on $Σ_2$, 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_15965 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Topological-Holomorphic ${\mathcal N} =4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-topological Strings Ong, Zhi-Cong Tan, Meng-Chwan High Energy Physics - Theory Algebraic Geometry Differential Geometry Quantum Algebra Representation Theory We perform a topological-holomorphic twist of $\mathcal{N}=4$ supersymmetric gauge theory on a four-manifold of the form $M_4=Σ_1 \times Σ_2$ with Riemann surfaces $Σ_{1,2}$, 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 $Σ_1$ whence we can dimensionally reduce it to 2d, via the effective sigma-model on $Σ_2$, 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. |
| title | Topological-Holomorphic ${\mathcal N} =4$ Gauge Theory: From Langlands Duality of Holomorphic Invariants to Mirror Symmetry of Quasi-topological Strings |
| topic | High Energy Physics - Theory Algebraic Geometry Differential Geometry Quantum Algebra Representation Theory |
| url | https://arxiv.org/abs/2305.15965 |