University of Maryland
Deligne pairings and holomorphic extension of analytic torsion
The purpose of this talk is to suggest an approach to certain constructions in hyperkähler geometry via Deligne pairings. I will discuss the concrete example of rank 1 Higgs bundles on a Riemann surface. The method produces a flat connection on a combination of determinant bundles over the de Rham moduli space. We show that the holomorphic extension of analytic torsion, introduced by Fay and used in this context by Hitchin, can be interpreted as a covariantly constant section of this bundle. The hyperholomorphic line bundle on the twistor space admits a meromorphic connection, and this also easily follows from this construction. This is joint work with Gerard Freixas i Montplet.