$\operatorname{Sp}(1)$-symmetric hyper-Kähler quantisation

Andersen, Jørgen Ellegaard; Malusà, Alessandro; Rembado, Gabriele

doi:10.48550/arxiv.2111.03584

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Kähler Polarisations1

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2022

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“…for a fixed τ ∈ T . The same authors have addressed this problem, in the case of a Sp(1)-symmetric hyper-Kähler manifold, in a recent preprint [9].…”

Section: Kähler Polarisationsmentioning

confidence: 99%

Genus-one complex quantum Chern–Simons theory

Andersen

Malusà

Rembado

2022

Journal of Symplectic Geometry

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We consider the geometric quantisation of Chern-Simons theory for closed genus-one surfaces and semisimple complex algebraic groups. First we introduce the natural complexified analogue of the Hitchin connection in Kähler quantisation, with polarisations coming from the nonabelian Hodge hyper-Kähler geometry of the moduli spaces of flat connections, thereby complementing the realpolarised approach of Witten. Then we consider the connection of Witten, and we identify it with the complexified Hitchin connection using a version of the Bargmann transform on polarised sections over the moduli spaces.

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“…for a fixed τ ∈ T . The same authors have addressed this problem, in the case of a Sp(1)-symmetric hyper-Kähler manifold, in a recent preprint [9].…”

Section: Kähler Polarisationsmentioning

confidence: 99%