Quantisation conditions of the quantum Hitchin system and the real geometric Langlands correspondence

2017/07/25 by Teschner, Joerg · 1 citation
#51XX #81XX #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1707.07873

Abstract

Single-valuedness of the eigenfunctions of the quantised Hitchin Hamiltonians is proposed as a natural quantisation condition. Separation of Variables can be used to relate the classification of eigenstates to the classification of projective structures with real holonomy. Using complex Fenchel-Nielsen coordinates one may reformulate the quantisation conditions in terms of the generating function for the variety of opers. These results are interpreted as a variant of the geometric Langlands correspondence.

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