Quantum Analytic Langlands Correspondence
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913811046334464 |
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| author | Gaiotto, Davide Teschner, Jörg |
| author_facet | Gaiotto, Davide Teschner, Jörg |
| contents | The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\cal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation of the Analytic Langlands Correspondence, and discuss its relations to quantum field theory. The partition functions of the $H_3^+$ WZNW model are interpreted as the wave-functions of a spherical vector in the quantisation of complex Chern-Simons theory. Verlinde line operators generate a representation of two copies of the quantised skein algebra on generalised partition functions. We conjecture that this action generates a basis for the underlying Hilbert space, and explain in which sense the resulting quantum theory represents a deformation of the Analytic Langlands Correspondence. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_00494 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quantum Analytic Langlands Correspondence Gaiotto, Davide Teschner, Jörg High Energy Physics - Theory Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\cal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation of the Analytic Langlands Correspondence, and discuss its relations to quantum field theory. The partition functions of the $H_3^+$ WZNW model are interpreted as the wave-functions of a spherical vector in the quantisation of complex Chern-Simons theory. Verlinde line operators generate a representation of two copies of the quantised skein algebra on generalised partition functions. We conjecture that this action generates a basis for the underlying Hilbert space, and explain in which sense the resulting quantum theory represents a deformation of the Analytic Langlands Correspondence. |
| title | Quantum Analytic Langlands Correspondence |
| topic | High Energy Physics - Theory Mathematical Physics Algebraic Geometry Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2402.00494 |