Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8255448 | Journal of Geometry and Physics | 2018 | 11 Pages |
Abstract
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,â¦,n, (generalized Grotendieck's dessins d'enfants) of fixed genus, degree, and the ramification profiles at two points, z1 and zn. Ramifications at other nâ2 points enter the sum with the length of the profile at z2
and with the total length of profiles at the remaining nâ3 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 tr MiMi+1â1. 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 1âN2. We discuss braid-group symmetries of our model and perspectives of the proposed method.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Jan Ambjørn, Leonid O. Chekhov,