2013/10/31 by Olivia Dumitrescu, Motohico Mulase · 1 citation
Mathematics · Physics and Astronomy · #math-ph #math.AG #math.MP #math.QA #math.SG #msc:14H15 #msc:14H60 #msc:14H81 #msc:34E20 #msc:81T45
paper · pdf · doi:10.1007/s11005-014-0679-0
published as Letters in Mathematical Physics 104, 635--671 (2014) · 34 pages
arxiv created 2014/01/14 · arxiv updated 2015/06/17
We generalize the topological recursion of Eynard-Orantin (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 ℏ-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 ℏ-deformed D-modules recovers the initial family of Hitchin spectral curves.