TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.18.4.144
TI  - Quantum analytic Langlands correspondence
PY  - 2025/04/30
UR  - https://www.scipost.org/SciPostPhys.18.4.144
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 18
IS  - 4
SP  - 144
A1  - Gaiotto, Davide
AU  - Teschner, Jörg
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.18.4.144,
	title={{Quantum analytic Langlands correspondence}},
	author={Davide Gaiotto and Jörg Teschner},
	journal={SciPost Phys.},
	volume={18},
	pages={144},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.18.4.144},
	url={https://scipost.org/10.21468/SciPostPhys.18.4.144},
}