UC Davis

We generalize the topological recursion of Eynard-Orantin (JHEP 0612:053, 2006; Commun Number Theory Phys 1:347-452, 2007) to the family of spectral curves of Hitchin fibrations. A spectral curve in the topological recursion, which is defined to be a complex plane curve, is replaced with a generic curve in the cotangent bundle T*C of an arbitrary smooth base curve C. We then prove that these spectral curves are quantizable, using the new formalism. More precisely, we construct the canonical generators of the formal h{stroke}-deformation family of D modules over an arbitrary projective algebraic curve C of genus greater than 1, from the geometry of a prescribed family of smooth Hitchin spectral curves associated with the SL(2, ℂ)-character variety of the fundamental group π1(C). We show that the semi-classical limit through the WKB approximation of these h{stroke}-deformed D modules recovers the initial family of Hitchin spectral curves. © 2014 Springer Science+Business Media Dordrecht.