2014/09/11 by Jan Ambjorn, J. Ambjørn, Leonid Chekhov +1 · 34 citations
Computer Science · Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Fixed point #Hurwitz matrix #Hypergeometric distribution #Polynomial and algebraic computation #Projective line #Ramification #Recursion (computer science) #hep-th #math-ph #math.CO #math.MP #msc:15B52
paper · pdf · doi:10.1007/s11232-014-0229-z
published in Theoretical and Mathematical Physics 181(3), 1486-1498 (Pleiades Publishing) · 12 pages, 2 figures in LaTeX, contribution to the volume of TMPh celebrating the 75th birthday of A A Slavnov
arxiv created 2014/09/11 · openalex publication_date 2014/12/01 · arxiv updated 2015/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We present the multi-matrix models that are the generating functions for 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. We take a sum over all possible ramifications at other n-2 points with the fixed length of the profile at z2 and with the fixed total length of profiles at the remaining n-3 points. All these models belong to a class of hypergeometric Hurwitz models thus being tau functions of the Kadomtsev--Petviashvili (KP) hierarchy. In the case described above, we can present the obtained model as a chain of matrices with a (nonstandard) nearest-neighbor interaction of the type \tr MiMi+1-1. We describe the technique for evaluating spectral curves of such models, which opens the possibility of applying the topological recursion for developing 1/N2-expansions of these model. These spectral curves turn out to be of an algebraic type.