1997/03/26 by Ivan K. Kostov, Ivan Kostov, Matthias Staudacher +1 · 1 citation
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #Combinatorics #Eigenvalues and eigenvectors #Lattice (music) #Limit (mathematics) #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Matrix model #Partition function (quantum field theory) #Physics #Pure mathematics #Quantum Chromodynamics and Particle Interactions #Quantum mechanics #Random matrix #Riemann surface #String (physics) #hep-th
paper · pdf · doi:10.1007/s002200050269
published as Commun.Math.Phys.191:283-298,1998 · 21 pages, 2 figures, TeX, harvmac.tex, epsf.tex, TeX "big"
arxiv created 1997/03/26 · openalex publication_date 1998/02/01 · arxiv updated 2014/11/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We present a complex matrix gauge model defined on an arbitrary two-dimensional orientable lattice. We rewrite the model's partition function in terms of a sum over representations of the group U(N). The model solves the general combinatorial problem of counting branched covers of orientable Riemann surfaces with any given, fixed branch point structure. We then define an appropriate continuum limit allowing the branch points to freely float over the surface. The simplest such limit reproduces two-dimensional chiral U(N) Yang-Mills theory and its string description due to Gross and Taylor.