2023/01/15 by S. Hikami, Hikami, Shinobu
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Geometric and Algebraic Topology #Mathematical Physics (math-ph) #Theoretical and Computational Physics #Topological and Geometric Data Analysis
paper · pdf · doi:10.48550/arxiv.2301.06003
openalex publication_date 2023/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A classical knot is described by a one-stroke trajectory with entanglements of a string. The replica method appears as a powerful tool in statistical mechanics for a polymer or self-avoiding walk. We consider this replica N to 0 limit in Gaussian means of the products of trace of N x N Hermitian matrices, which provides one-stroke graphs of a knot. The Seifert surfaces of knots and links are derived by a random matrix model. The zeros of Alexander polynomials on a unit circle are discussed for the case of n-vertices in the analogy of Yang-Lee edge singularity. The extension of one matrix model is considered for higher dimensional knots and for half integral level k in Chern-Simons gauge theory.