2005/06/30 by Tigran Sedrakyan, T. A. Sedrakyan
Chemistry · Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Molecular spectroscopy and chirality #Random Matrices and Applications #cond-mat.dis-nn #cond-mat.mes-hall #hep-th #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1016/j.nuclphysb.2005.09.020
published as Nucl.Phys. B729 (2005) 526-541 · 13 pages, 2 figures, Revtex
openalex publication_date 2005/10/04 · arxiv created 2005/10/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct a replica field theory for a random matrix model with logarithmic confinement [K.A.Muttalib et.al., Phys. Rev. Lett. 71, 471 (1993)]. The corresponding replica partition function is calculated exactly for any size of matrix N. We make a color-flavor transformation of the original model and find corresponding Toda lattice equations for the replica partition function in both formulations. The replica partition function in the flavor space is defined by generalized Itzikson-Zuber (IZ) integral over homogeneous factor space of pseudo-unitary supergroups SU(n| M,M)/SU(n| M-N,M) (Stiefel manifold) with M→∞, which is evaluated and represented in a compact form.