2018/06/18 by J. Ambjørn, Jan Ambjørn, Leonid Chekhov +1 · 4 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic curve #Algebraic structures and combinatorial models #Combinatorics #Fixed point #Generating function #Genus #Geometry #Hermitian matrix #Homogeneous space #Mathematical analysis #Mathematics #Projective line #Pure mathematics #hep-th #math-ph #math.AG #math.MP #msc:05C30 #msc:15B52
paper · pdf · doi:10.1016/j.geomphys.2018.07.004
published in Journal of Geometry and Physics 132, 382-392 (Elsevier BV) · 13 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:1409.3553
arxiv created 2018/06/18 · openalex created_date 2018/06/29 · openalex publication_date 2018/07/23 · arxiv updated 2018/08/15 · openalex updated_date 2026/08/05
We consider multi-matrix models that are generating functions for the numbers of branched covers of the complex projective line ramified over n fixed points zi, i=1,…,n, (generalized Grotendieck's dessins d'enfants) of fixed genus, degree, and the ramification profiles at two points, z1 and zn. Ramifications at other n-2 points enter the sum with the length of the profile at z2 and with the total length of profiles at the remaining n-3 points. We find the spectral curve of the model for n=5 using the loop equation technique for the above generating function represented as a chain of Hermitian matrices with a nearest-neighbor interaction of the type trMiMi+1-1. The obtained spectral curve is algebraic and provides all necessary ingredients for the topological recursion procedure producing all-genus terms of the asymptotic expansion of our model in 1/N2. We discuss braid-group symmetries of our model and perspectives of the proposed method.