2018/01/25 by Marianne Leitner, Leitner, Marianne · 1 citation
Mathematics · Physics and Astronomy · #11F03 (Primary) #57M50 #81T40 (Secondary) #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Quantum Algebra (math.QA) #hep-th #math.QA #msc:11F03 #msc:57M50 #msc:81T40
paper · pdf · doi:10.48550/arxiv.1801.08387
53 pages. The title is modified. Better organisation of the expansions, and comment on the period matrix included
openalex publication_date 2018/01/25 · arxiv created 2021/06/15 · arxiv updated 2021/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the (2,5) minimal model, the partition function for genus g=2 Riemann surfaces is given by a 5-tuple of functions with appropriate transformation under the mapping class group. These functions generalise the two Rogers-Ramanujan functions for the torus. Their expansions around a locus of surfaces with conical singularities in the interior of the g=2 Siegel upper half plane are obtained in terms of standard modular forms. The dependence on the metric is controlled by a canonical choice of flat surface metrics. In the alternative case where a handle of the g=2 surface is pinched, our method requires knowledge of the two-point function of the fundamental lowest-weight vector in the non-vacuum representation of the Virasoro algebra, for which we derive a 3\tsrd order ODE. In order to make the paper more accessible to mathematicians, the exposition includes a short introduction to conformal field theory on Riemann surfaces, which may be of independent interest.