Duality and integrability of a supermatrix model with an external source

2014/10/31 by Taro Kimura, T. Kimura · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Characteristic polynomial #Duality (order theory) #Hermitian matrix #Matrix (chemical analysis) #Polynomial #Random Matrices and Applications #Supermatrix #Toda lattice #cond-mat.stat-mech #hep-th #math-ph #math.MP

paper · pdf · doi:10.1093/ptep/ptu163

published in Progress of Theoretical and Experimental Physics 2014(12), 123A01 (University of Oxford) · 1+15 pages, 1 figure; typos corrected

openalex publication_date 2014/12/10 · arxiv created 2014/12/14 · arxiv updated 2014/12/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

We study the Hermitian supermatrix model involving an external source. We derive the determinantal formula for the supermatrix partition function, and also for the expectation value of the characteristic polynomial ratio, which yields the duality between the characteristic polynomial and the external source with an arbitrary matrix potential function. We also show that the supermatrix integral satisfies the 1- and 2D Toda lattice equations as well as the ordinary matrix model.

Citations

• Universal Results for Correlations of Characteristic Polynomials: Riemann-Hilbert Approach
• Supermatrix models, loop equations, and duality
• Note on a duality of topological branes