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Quantum Analytic Langlands Correspondence
by Davide Gaiotto, Jörg Teschner
Submission summary
| Authors (as registered SciPost users): | Davide Gaiotto |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2402.00494v1 (pdf) |
| Date submitted: | 2024-10-31 23:58 |
| Submitted by: | Gaiotto, Davide |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
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.
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