Aarhus University Seal / Aarhus Universitets segl

Hitchin's connection in metaplectic quantization

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

  • Jørgen Ellegaard Andersen, Denmark
  • Niels Leth Gammelgaard, Denmark
  • Magnus Roed Lauridsen, Denmark
We give a differential geometric construction of a connection, which we call the Hitchin connection, in the bundle of quantum Hilbert spaces arising from metaplectically corrected geometric quantization of a prequantizable, symplectic manifold, endowed with a rigid family of Kähler structures, all of which give vanishing first Dolbeault cohomology groups.

This generalizes work of both Hitchin, Scheinost and Schottenloher, and Andersen, since our construction does not need that the first Chern class is proportional to the class of the symplectic form, nor do we need compactness of the symplectic manifold in question.

Furthermore, when we are in a setting similar to the moduli space, we give an explicit formula and show that this connection agrees with previous constructions.
Original languageEnglish
JournalQuantum Topology
Volume3
Issue3/4
Pages (from-to)327-357
ISSN1663-487X
DOIs
Publication statusPublished - 2012

    Research areas

  • Geometric quantization, metaplectic correction, complex manifolds

See relations at Aarhus University Citationformats

ID: 45642569