The Hitchin-Witten Connection and Complex Quantum Chern-Simons Theory
arXiv:1409.1035
Abstract
We give a direct calculation of the curvature of the Hitchin connection, in geometric quantization on a symplectic manifold, using only differential geometric techniques. In particular, we establish that the curvature acts as a first-order operator on the quantum spaces. Projective flatness follows if the Kähler structures do not admit holomorphic vector fields. Following Witten, we define a complex variant of the Hitchin connection on the bundle of prequantum spaces. The curvature is essentially unchanged, so projective flatness holds in the same cases. Finally, the results are applied to quantum Chern-Simons theory, both for compact and complex gauge groups.
References in corpus (5)
- Generalized Volume Conjecture and the A-Polynomials -- the Neumann-Zagier Potential Function as a Classical Limit of Quantum Invariant
- SL(2,C) Chern-Simons theory and the asymptotic behavior of the colored Jones polynomial
- Complex Quantum Chern-Simons
- Asymptotics of Toeplitz operators and applications in TQFT
- Complex Chern-Simons theory at level k via the 3d-3d correspondence