Jørgen E. Andersen and his former PhD student, Alessandro Malusà, gets a paper accepted in Letters in Mathematical Physics
2019.01.22 |
The paper by Andersen and Malusà (University of Saskatchewan); Asymptotic properties of the Hitchin–Witten connection was accepted yesterday in Letters in Mathematical Physics.
In this paper the authors explore extensions to SL(n,C)-Chern-Simons theory of some results obtained for SU(n)-Chern-Simons theory via the asymptotic properties of the Hitchin connection and its relation to Toeplitz operators developed previously by the first named author. They define a formal Hitchin-Witten connection for the imaginary part s of the quantum parameter t=k+is and investigate the existence of a formal trivialisation. After reducing the problem to a recursive system of differential equations, they identify a cohomological obstruction to the existence of a solution. They explicitly find one for the first step, in the specific case of an operator of order 0, and show in general the vanishing of a weakened version of the obstruction. They also find a solution of the whole recursion in the case of a surface of genus 1.
Link to arXiv: https://arxiv.org/abs/1805.04868
