Quantum analytic Langlands correspondence
The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\mathcal{N}=4$ super Yang-Mills theory. We propose a one-parameter deformation of the Analytic Langlands Correspondence, and discuss its rel...
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2025-04-01
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| Series: | SciPost Physics |
| Online Access: | https://scipost.org/SciPostPhys.18.4.144 |
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| author | Davide Gaiotto, Jörg Teschner |
| author_facet | Davide Gaiotto, Jörg Teschner |
| author_sort | Davide Gaiotto, Jörg Teschner |
| collection | DOAJ |
| description | The analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\mathcal{N}=4$ 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 | Article |
| id | doaj-art-b5366d908eae48cfaabdefba7dab5599 |
| institution | Kabale University |
| issn | 2542-4653 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | SciPost |
| record_format | Article |
| series | SciPost Physics |
| spelling | doaj-art-b5366d908eae48cfaabdefba7dab55992025-08-20T03:53:39ZengSciPostSciPost Physics2542-46532025-04-0118414410.21468/SciPostPhys.18.4.144Quantum analytic Langlands correspondenceDavide Gaiotto, Jörg TeschnerThe analytic Langlands correspondence describes the solution to the spectral problem for the quantised Hitchin Hamiltonians. It is related to the S-duality of $\mathcal{N}=4$ 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.https://scipost.org/SciPostPhys.18.4.144 |
| spellingShingle | Davide Gaiotto, Jörg Teschner Quantum analytic Langlands correspondence SciPost Physics |
| title | Quantum analytic Langlands correspondence |
| title_full | Quantum analytic Langlands correspondence |
| title_fullStr | Quantum analytic Langlands correspondence |
| title_full_unstemmed | Quantum analytic Langlands correspondence |
| title_short | Quantum analytic Langlands correspondence |
| title_sort | quantum analytic langlands correspondence |
| url | https://scipost.org/SciPostPhys.18.4.144 |
| work_keys_str_mv | AT davidegaiottojorgteschner quantumanalyticlanglandscorrespondence |